{"id":119,"date":"2018-12-20T09:35:19","date_gmt":"2018-12-20T09:35:19","guid":{"rendered":"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=119"},"modified":"2018-12-20T09:48:06","modified_gmt":"2018-12-20T09:48:06","slug":"borel-cantelli-lemma","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/chapter\/borel-cantelli-lemma\/","title":{"rendered":"Borel-Cantelli lemma"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/r2kFX91Fv68\" 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-134\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-1-1.jpg\" alt=\"\" width=\"1257\" height=\"1373\" \/> <img class=\"aligncenter size-full wp-image-122\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-2.jpg\" alt=\"\" width=\"1307\" height=\"1521\" \/> <img class=\"aligncenter size-full wp-image-123\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-3.jpg\" alt=\"\" width=\"1259\" height=\"1589\" \/> <img class=\"aligncenter size-full wp-image-124\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-4.jpg\" alt=\"\" width=\"1271\" height=\"1661\" \/> <img class=\"aligncenter size-full wp-image-125\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-5.jpg\" alt=\"\" width=\"1261\" height=\"1621\" \/> <img class=\"aligncenter size-full wp-image-126\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-6.jpg\" alt=\"\" width=\"1241\" height=\"1567\" \/> <img class=\"aligncenter size-full wp-image-127\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-7.jpg\" alt=\"\" width=\"1287\" height=\"1623\" \/> <img class=\"aligncenter size-full wp-image-128\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-8.jpg\" alt=\"\" width=\"1239\" height=\"1137\" \/>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Borel-Cantelli lemma<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/r2kFX91Fv68\" 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\n<img class=\"aligncenter size-full wp-image-131\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235105Borel-CantelliLemma_Ref-1.jpg\" alt=\"\" width=\"1175\" height=\"745\" \/>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/r2kFX91Fv68\" 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-134\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-1-1.jpg\" alt=\"\" width=\"1257\" height=\"1373\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-1-1.jpg 1257w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-1-1-275x300.jpg 275w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-1-1-768x839.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-1-1-937x1024.jpg 937w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-1-1-65x71.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-1-1-225x246.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-1-1-350x382.jpg 350w\" sizes=\"auto, (max-width: 1257px) 100vw, 1257px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-122\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-2.jpg\" alt=\"\" width=\"1307\" height=\"1521\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-2.jpg 1307w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-2-258x300.jpg 258w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-2-768x894.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-2-880x1024.jpg 880w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-2-65x76.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-2-225x262.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-2-350x407.jpg 350w\" sizes=\"auto, (max-width: 1307px) 100vw, 1307px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-123\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-3.jpg\" alt=\"\" width=\"1259\" height=\"1589\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-3.jpg 1259w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-3-238x300.jpg 238w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-3-768x969.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-3-811x1024.jpg 811w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-3-65x82.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-3-225x284.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-3-350x442.jpg 350w\" sizes=\"auto, (max-width: 1259px) 100vw, 1259px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-124\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-4.jpg\" alt=\"\" width=\"1271\" height=\"1661\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-4.jpg 1271w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-4-230x300.jpg 230w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-4-768x1004.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-4-784x1024.jpg 784w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-4-65x85.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-4-225x294.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-4-350x457.jpg 350w\" sizes=\"auto, (max-width: 1271px) 100vw, 1271px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-125\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-5.jpg\" alt=\"\" width=\"1261\" height=\"1621\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-5.jpg 1261w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-5-233x300.jpg 233w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-5-768x987.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-5-797x1024.jpg 797w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-5-65x84.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-5-225x289.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-5-350x450.jpg 350w\" sizes=\"auto, (max-width: 1261px) 100vw, 1261px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-126\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-6.jpg\" alt=\"\" width=\"1241\" height=\"1567\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-6.jpg 1241w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-6-238x300.jpg 238w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-6-768x970.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-6-811x1024.jpg 811w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-6-65x82.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-6-225x284.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-6-350x442.jpg 350w\" sizes=\"auto, (max-width: 1241px) 100vw, 1241px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-127\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-7.jpg\" alt=\"\" width=\"1287\" height=\"1623\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-7.jpg 1287w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-7-238x300.jpg 238w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-7-768x969.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-7-812x1024.jpg 812w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-7-65x82.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-7-225x284.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-7-350x441.jpg 350w\" sizes=\"auto, (max-width: 1287px) 100vw, 1287px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-128\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-8.jpg\" alt=\"\" width=\"1239\" height=\"1137\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-8.jpg 1239w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-8-300x275.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-8-768x705.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-8-1024x940.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-8-65x60.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-8-225x206.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235099Borel-CantelliLemma-8-350x321.jpg 350w\" sizes=\"auto, (max-width: 1239px) 100vw, 1239px\" \/><\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Borel-Cantelli lemma<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/r2kFX91Fv68\" 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><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-131\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235105Borel-CantelliLemma_Ref-1.jpg\" alt=\"\" width=\"1175\" height=\"745\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235105Borel-CantelliLemma_Ref-1.jpg 1175w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235105Borel-CantelliLemma_Ref-1-300x190.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235105Borel-CantelliLemma_Ref-1-768x487.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235105Borel-CantelliLemma_Ref-1-1024x649.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235105Borel-CantelliLemma_Ref-1-65x41.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235105Borel-CantelliLemma_Ref-1-225x143.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522235105Borel-CantelliLemma_Ref-1-350x222.jpg 350w\" sizes=\"auto, (max-width: 1175px) 100vw, 1175px\" \/><\/p>\n","protected":false},"author":3,"menu_order":8,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-119","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/pressbooks\/v2\/chapters\/119","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":6,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/pressbooks\/v2\/chapters\/119\/revisions"}],"predecessor-version":[{"id":135,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/pressbooks\/v2\/chapters\/119\/revisions\/135"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/pressbooks\/v2\/chapters\/119\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/wp\/v2\/media?parent=119"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/pressbooks\/v2\/chapter-type?post=119"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/wp\/v2\/contributor?post=119"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/wp\/v2\/license?post=119"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}