{"id":315,"date":"2018-12-20T09:00:35","date_gmt":"2018-12-20T09:00:35","guid":{"rendered":"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=315"},"modified":"2018-12-20T09:00:35","modified_gmt":"2018-12-20T09:00:35","slug":"continuity-theorem","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/chapter\/continuity-theorem\/","title":{"rendered":"Continuity Theorem"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/uFrylTX7mAk\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter wp-image-316\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-80.png\" alt=\"\" width=\"585\" height=\"307\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-317\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1.png\" alt=\"\" width=\"431\" height=\"279\" \/> <img class=\"aligncenter size-full wp-image-318\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/2.png\" alt=\"\" width=\"388\" height=\"427\" \/> <img class=\"aligncenter size-full wp-image-319\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/3.png\" alt=\"\" width=\"382\" height=\"522\" \/> <img class=\"aligncenter size-full wp-image-320\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/4.png\" alt=\"\" width=\"449\" height=\"351\" \/> <img class=\"aligncenter size-full wp-image-321\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/5.png\" alt=\"\" width=\"461\" height=\"307\" \/> <img class=\"aligncenter size-full wp-image-322\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/6.png\" alt=\"\" width=\"447\" height=\"514\" \/> <img class=\"aligncenter size-full wp-image-323\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/7.png\" alt=\"\" width=\"347\" height=\"449\" \/> <img class=\"aligncenter size-full wp-image-324\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/8.png\" alt=\"\" width=\"327\" height=\"502\" \/> <img class=\"aligncenter size-full wp-image-325\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/9.png\" alt=\"\" width=\"415\" height=\"223\" \/> <img class=\"aligncenter size-full wp-image-326\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/10.png\" alt=\"\" width=\"425\" height=\"315\" \/> <img class=\"aligncenter size-full wp-image-327\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/11.png\" alt=\"\" width=\"413\" height=\"445\" \/> <img class=\"aligncenter size-full wp-image-328\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/12.png\" alt=\"\" width=\"420\" height=\"521\" \/> <img class=\"aligncenter size-full wp-image-329\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/13.png\" alt=\"\" width=\"416\" height=\"400\" \/> <img class=\"aligncenter wp-image-330\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/14.png\" alt=\"\" width=\"413\" height=\"436\" \/> <img class=\"aligncenter size-full wp-image-331\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/15.png\" alt=\"\" width=\"347\" height=\"372\" \/> <img class=\"aligncenter size-full wp-image-332\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/16.png\" alt=\"\" width=\"315\" height=\"460\" \/> <img class=\"aligncenter size-full wp-image-333\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/17.png\" alt=\"\" width=\"312\" height=\"499\" \/> <img class=\"aligncenter size-full wp-image-334\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/18.png\" alt=\"\" width=\"498\" height=\"410\" \/>\r\n<div>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Continuity Theorem<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/uFrylTX7mAk\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nReferences\r\n\r\n&nbsp;\r\n\r\n1.\u00a0\u00a0 TM Apostol: Mathematical Analysis.\r\n\r\n2.\u00a0\u00a0 AK Basu: Measure Theory and Probability.\r\n\r\n3.\u00a0\u00a0 P Billingsley: Probability and Measure.\r\n\r\n4.\u00a0\u00a0 KL Chung: A Course in Probability Theory.\r\n\r\n5.\u00a0\u00a0 W Feller: An Introduction to Probability Theory and its Applications, Vol-I.\r\n\r\n6.\u00a0\u00a0 AM Gun, MK Gupta, B Dasgupta: An Outline of Statistical Theory, Vol -I.\r\n\r\n7.\u00a0\u00a0 E Luckacs, RG Laha: Applications of Characteristic Functions.\r\n\r\n8.\u00a0\u00a0 E Parzen: Modern Probability Theory and its Applications.\r\n\r\n9.\u00a0\u00a0 RJ Ser ing: Approximation Theorems of Mathematical Statistics.\r\n\r\n10.\u00a0 W Rudin: Principles of Mathematical Analysis.\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/uFrylTX7mAk\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-316\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-80.png\" alt=\"\" width=\"585\" height=\"307\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-80.png 335w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-80-300x158.png 300w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-80-65x34.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/Untitled-80-225x118.png 225w\" sizes=\"auto, (max-width: 585px) 100vw, 585px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-317\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1.png\" alt=\"\" width=\"431\" height=\"279\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1.png 431w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1-300x194.png 300w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1-65x42.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1-225x146.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1-350x227.png 350w\" sizes=\"auto, (max-width: 431px) 100vw, 431px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-318\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/2.png\" alt=\"\" width=\"388\" height=\"427\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/2.png 388w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/2-273x300.png 273w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/2-65x72.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/2-225x248.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/2-350x385.png 350w\" sizes=\"auto, (max-width: 388px) 100vw, 388px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-319\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/3.png\" alt=\"\" width=\"382\" height=\"522\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/3.png 382w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/3-220x300.png 220w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/3-65x89.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/3-225x307.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/3-350x478.png 350w\" sizes=\"auto, (max-width: 382px) 100vw, 382px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-320\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/4.png\" alt=\"\" width=\"449\" height=\"351\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/4.png 449w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/4-300x235.png 300w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/4-65x51.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/4-225x176.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/4-350x274.png 350w\" sizes=\"auto, (max-width: 449px) 100vw, 449px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-321\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/5.png\" alt=\"\" width=\"461\" height=\"307\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/5.png 461w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/5-300x200.png 300w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/5-65x43.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/5-225x150.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/5-350x233.png 350w\" sizes=\"auto, (max-width: 461px) 100vw, 461px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-322\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/6.png\" alt=\"\" width=\"447\" height=\"514\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/6.png 447w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/6-261x300.png 261w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/6-65x75.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/6-225x259.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/6-350x402.png 350w\" sizes=\"auto, (max-width: 447px) 100vw, 447px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-323\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/7.png\" alt=\"\" width=\"347\" height=\"449\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/7.png 347w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/7-232x300.png 232w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/7-65x84.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/7-225x291.png 225w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-324\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/8.png\" alt=\"\" width=\"327\" height=\"502\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/8.png 327w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/8-195x300.png 195w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/8-65x100.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/8-225x345.png 225w\" sizes=\"auto, (max-width: 327px) 100vw, 327px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-325\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/9.png\" alt=\"\" width=\"415\" height=\"223\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/9.png 415w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/9-300x161.png 300w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/9-65x35.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/9-225x121.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/9-350x188.png 350w\" sizes=\"auto, (max-width: 415px) 100vw, 415px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-326\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/10.png\" alt=\"\" width=\"425\" height=\"315\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/10.png 425w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/10-300x222.png 300w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/10-65x48.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/10-225x167.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/10-350x259.png 350w\" sizes=\"auto, (max-width: 425px) 100vw, 425px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-327\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/11.png\" alt=\"\" width=\"413\" height=\"445\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/11.png 413w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/11-278x300.png 278w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/11-65x70.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/11-225x242.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/11-350x377.png 350w\" sizes=\"auto, (max-width: 413px) 100vw, 413px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-328\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/12.png\" alt=\"\" width=\"420\" height=\"521\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/12.png 420w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/12-242x300.png 242w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/12-65x81.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/12-225x279.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/12-350x434.png 350w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-329\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/13.png\" alt=\"\" width=\"416\" height=\"400\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/13.png 416w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/13-300x288.png 300w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/13-65x63.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/13-225x216.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/13-350x337.png 350w\" sizes=\"auto, (max-width: 416px) 100vw, 416px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-330\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/14.png\" alt=\"\" width=\"413\" height=\"436\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/14.png 234w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/14-65x69.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/14-225x238.png 225w\" sizes=\"auto, (max-width: 413px) 100vw, 413px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-331\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/15.png\" alt=\"\" width=\"347\" height=\"372\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/15.png 347w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/15-280x300.png 280w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/15-65x70.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/15-225x241.png 225w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-332\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/16.png\" alt=\"\" width=\"315\" height=\"460\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/16.png 315w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/16-205x300.png 205w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/16-65x95.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/16-225x329.png 225w\" sizes=\"auto, (max-width: 315px) 100vw, 315px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-333\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/17.png\" alt=\"\" width=\"312\" height=\"499\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/17.png 312w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/17-188x300.png 188w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/17-65x104.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/17-225x360.png 225w\" sizes=\"auto, (max-width: 312px) 100vw, 312px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-334\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/18.png\" alt=\"\" width=\"498\" height=\"410\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/18.png 498w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/18-300x247.png 300w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/18-65x54.png 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/18-225x185.png 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/18-350x288.png 350w\" sizes=\"auto, (max-width: 498px) 100vw, 498px\" \/><\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Continuity Theorem<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/uFrylTX7mAk\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>References<\/p>\n<p>&nbsp;<\/p>\n<p>1.\u00a0\u00a0 TM Apostol: Mathematical Analysis.<\/p>\n<p>2.\u00a0\u00a0 AK Basu: Measure Theory and Probability.<\/p>\n<p>3.\u00a0\u00a0 P Billingsley: Probability and Measure.<\/p>\n<p>4.\u00a0\u00a0 KL Chung: A Course in Probability Theory.<\/p>\n<p>5.\u00a0\u00a0 W Feller: An Introduction to Probability Theory and its Applications, Vol-I.<\/p>\n<p>6.\u00a0\u00a0 AM Gun, MK Gupta, B Dasgupta: An Outline of Statistical Theory, Vol -I.<\/p>\n<p>7.\u00a0\u00a0 E Luckacs, RG Laha: Applications of Characteristic Functions.<\/p>\n<p>8.\u00a0\u00a0 E Parzen: Modern Probability Theory and its Applications.<\/p>\n<p>9.\u00a0\u00a0 RJ Ser ing: Approximation Theorems of Mathematical Statistics.<\/p>\n<p>10.\u00a0 W Rudin: Principles of Mathematical Analysis.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"author":3,"menu_order":19,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["mr-samopriya-basu"],"pb_section_license":""},"chapter-type":[],"contributor":[59],"license":[],"class_list":["post-315","chapter","type-chapter","status-publish","hentry","contributor-mr-samopriya-basu"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/315","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":1,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/315\/revisions"}],"predecessor-version":[{"id":335,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/315\/revisions\/335"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/315\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/media?parent=315"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapter-type?post=315"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/contributor?post=315"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/license?post=315"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}