{"id":451,"date":"2018-12-21T04:34:43","date_gmt":"2018-12-21T04:34:43","guid":{"rendered":"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=451"},"modified":"2018-12-21T04:37:04","modified_gmt":"2018-12-21T04:37:04","slug":"convergence-related-results-i","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/chapter\/convergence-related-results-i\/","title":{"rendered":"Convergence &amp; related results &#8211; I"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/fsb9GmwVl-Y\" 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<img class=\"aligncenter size-full wp-image-452\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-01.jpg\" alt=\"\" width=\"1265\" height=\"1669\" \/> <img class=\"aligncenter size-full wp-image-453\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-02.jpg\" alt=\"\" width=\"1233\" height=\"1617\" \/> <img class=\"aligncenter size-full wp-image-454\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-03.jpg\" alt=\"\" width=\"1313\" height=\"1633\" \/> <img class=\"aligncenter size-full wp-image-455\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-04.jpg\" alt=\"\" width=\"1273\" height=\"1673\" \/> <img class=\"aligncenter size-full wp-image-456\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-05.jpg\" alt=\"\" width=\"1241\" height=\"1561\" \/> <img class=\"aligncenter size-full wp-image-457\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-06.jpg\" alt=\"\" width=\"1253\" height=\"1569\" \/> <img class=\"aligncenter size-full wp-image-458\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-07.jpg\" alt=\"\" width=\"1253\" height=\"1617\" \/> <img class=\"aligncenter size-full wp-image-459\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-08.jpg\" alt=\"\" width=\"1313\" height=\"1609\" \/> <img class=\"aligncenter size-full wp-image-460\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-09.jpg\" alt=\"\" width=\"1245\" height=\"1529\" \/> <img class=\"aligncenter size-full wp-image-461\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-10.jpg\" alt=\"\" width=\"1309\" height=\"1493\" \/> <img class=\"aligncenter size-full wp-image-462\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-11.jpg\" alt=\"\" width=\"1700\" height=\"2200\" \/> <img class=\"aligncenter size-full wp-image-463\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-12.jpg\" alt=\"\" width=\"1241\" height=\"1597\" \/> <img class=\"aligncenter size-full wp-image-464\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-13.jpg\" alt=\"\" width=\"1257\" height=\"897\" \/>\r\n\r\n&nbsp;\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Convergence &amp; related results - I <\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/fsb9GmwVl-Y\" 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<ol>\r\n \t<li>TM Apostol: Mathematical Analysis.<\/li>\r\n \t<li>AK Basu: Measure Theory and Probability.<\/li>\r\n \t<li>P Billingsley: Probability and Measure.<\/li>\r\n \t<li>KL Chung: A Course in Probability Theory.<\/li>\r\n \t<li>W Feller: An Introduction to Probability Theory and its Applications, Vol-I.<\/li>\r\n \t<li>AM Gun, MK Gupta, B Dasgupta: An Outline of Statistical Theory, Vol -I.<\/li>\r\n \t<li>E Luckacs, RG Laha: Applications of Characteristic Functions.<\/li>\r\n \t<li>E Parzen: Modern Probability Theory and its Applications.<\/li>\r\n \t<li>RJ Ser ing: Approximation Theorems of Mathematical Statistics.<\/li>\r\n \t<li>W Rudin: Principles of Mathematical Analysis<\/li>\r\n<\/ol>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/fsb9GmwVl-Y\" 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><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-452\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-01.jpg\" alt=\"\" width=\"1265\" height=\"1669\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-01.jpg 1265w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-01-227x300.jpg 227w, 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src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-12.jpg\" alt=\"\" width=\"1241\" height=\"1597\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-12.jpg 1241w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-12-233x300.jpg 233w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-12-768x988.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-12-796x1024.jpg 796w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-12-65x84.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-12-225x290.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-12-350x450.jpg 350w\" sizes=\"auto, (max-width: 1241px) 100vw, 1241px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-464\" src=\"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-13.jpg\" alt=\"\" width=\"1257\" height=\"897\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-13.jpg 1257w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-13-300x214.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-13-768x548.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-13-1024x731.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-13-65x46.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-13-225x161.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-content\/uploads\/sites\/125\/2018\/12\/1522228889ConvergenceandrelatedResults-1-13-350x250.jpg 350w\" sizes=\"auto, (max-width: 1257px) 100vw, 1257px\" \/><\/p>\n<p>&nbsp;<\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Convergence &amp; related results &#8211; I <\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/fsb9GmwVl-Y\" 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<ol>\n<li>TM Apostol: Mathematical Analysis.<\/li>\n<li>AK Basu: Measure Theory and Probability.<\/li>\n<li>P Billingsley: Probability and Measure.<\/li>\n<li>KL Chung: A Course in Probability Theory.<\/li>\n<li>W Feller: An Introduction to Probability Theory and its Applications, Vol-I.<\/li>\n<li>AM Gun, MK Gupta, B Dasgupta: An Outline of Statistical Theory, Vol -I.<\/li>\n<li>E Luckacs, RG Laha: Applications of Characteristic Functions.<\/li>\n<li>E Parzen: Modern Probability Theory and its Applications.<\/li>\n<li>RJ Ser ing: Approximation Theorems of Mathematical Statistics.<\/li>\n<li>W Rudin: Principles of Mathematical Analysis<\/li>\n<\/ol>\n","protected":false},"author":3,"menu_order":31,"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-451","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\/451","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\/451\/revisions"}],"predecessor-version":[{"id":465,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/451\/revisions\/465"}],"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\/451\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/media?parent=451"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapter-type?post=451"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/contributor?post=451"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/license?post=451"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}