{"id":309,"date":"2018-12-21T05:59:31","date_gmt":"2018-12-21T05:59:31","guid":{"rendered":"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=309"},"modified":"2018-12-21T06:43:35","modified_gmt":"2018-12-21T06:43:35","slug":"product-measure-spaces-and-the-fubini-tonelli-theorem","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/chapter\/product-measure-spaces-and-the-fubini-tonelli-theorem\/","title":{"rendered":"Product Measure Spaces and the Fubini-Tonelli Theorem"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/WhZJBPdueeM\" 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-311\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-1.jpg\" alt=\"\" width=\"1395\" height=\"1735\" \/> <img class=\"aligncenter size-full wp-image-312\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-2.jpg\" alt=\"\" width=\"1397\" height=\"1959\" \/> <img class=\"aligncenter size-full wp-image-313\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-3.jpg\" alt=\"\" width=\"1421\" height=\"1941\" \/> <img class=\"aligncenter size-full wp-image-314\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-4.jpg\" alt=\"\" width=\"1345\" height=\"1787\" \/> <img class=\"aligncenter size-full wp-image-315\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-5.jpg\" alt=\"\" width=\"1421\" height=\"1907\" \/>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Product Measure Spaces and the Fubini-Tonelli Theorem<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/WhZJBPdueeM\" 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-318\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304907ProductSpaceProductMeasureFubinisTheorem_Ref-1.jpg\" alt=\"\" width=\"1199\" height=\"757\" \/>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/WhZJBPdueeM\" 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-311\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-1.jpg\" alt=\"\" width=\"1395\" height=\"1735\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-1.jpg 1395w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-1-241x300.jpg 241w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-1-768x955.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-1-823x1024.jpg 823w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-1-65x81.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-1-225x280.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-1-350x435.jpg 350w\" sizes=\"auto, (max-width: 1395px) 100vw, 1395px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-312\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-2.jpg\" alt=\"\" width=\"1397\" height=\"1959\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-2.jpg 1397w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-2-214x300.jpg 214w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-2-768x1077.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-2-730x1024.jpg 730w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-2-65x91.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-2-225x316.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-2-350x491.jpg 350w\" sizes=\"auto, (max-width: 1397px) 100vw, 1397px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-313\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-3.jpg\" alt=\"\" width=\"1421\" height=\"1941\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-3.jpg 1421w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-3-220x300.jpg 220w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-3-768x1049.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-3-750x1024.jpg 750w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-3-65x89.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-3-225x307.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-3-350x478.jpg 350w\" sizes=\"auto, (max-width: 1421px) 100vw, 1421px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-314\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-4.jpg\" alt=\"\" width=\"1345\" height=\"1787\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-4.jpg 1345w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-4-226x300.jpg 226w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-4-768x1020.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-4-771x1024.jpg 771w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-4-65x86.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-4-225x299.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-4-350x465.jpg 350w\" sizes=\"auto, (max-width: 1345px) 100vw, 1345px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-315\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-5.jpg\" alt=\"\" width=\"1421\" height=\"1907\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-5.jpg 1421w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-5-224x300.jpg 224w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-5-768x1031.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-5-763x1024.jpg 763w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-5-65x87.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-5-225x302.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304902ProductSpaceProductMeasureFubinisTheorem-5-350x470.jpg 350w\" sizes=\"auto, (max-width: 1421px) 100vw, 1421px\" \/><\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Product Measure Spaces and the Fubini-Tonelli Theorem<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/WhZJBPdueeM\" 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-318\" src=\"http:\/\/statp02.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304907ProductSpaceProductMeasureFubinisTheorem_Ref-1.jpg\" alt=\"\" width=\"1199\" height=\"757\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304907ProductSpaceProductMeasureFubinisTheorem_Ref-1.jpg 1199w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304907ProductSpaceProductMeasureFubinisTheorem_Ref-1-300x189.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304907ProductSpaceProductMeasureFubinisTheorem_Ref-1-768x485.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304907ProductSpaceProductMeasureFubinisTheorem_Ref-1-1024x647.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304907ProductSpaceProductMeasureFubinisTheorem_Ref-1-65x41.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304907ProductSpaceProductMeasureFubinisTheorem_Ref-1-225x142.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-content\/uploads\/sites\/126\/2018\/12\/1522304907ProductSpaceProductMeasureFubinisTheorem_Ref-1-350x221.jpg 350w\" sizes=\"auto, (max-width: 1199px) 100vw, 1199px\" \/><\/p>\n","protected":false},"author":3,"menu_order":26,"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-309","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/pressbooks\/v2\/chapters\/309","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":4,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/pressbooks\/v2\/chapters\/309\/revisions"}],"predecessor-version":[{"id":319,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/pressbooks\/v2\/chapters\/309\/revisions\/319"}],"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\/309\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/wp\/v2\/media?parent=309"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/pressbooks\/v2\/chapter-type?post=309"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/wp\/v2\/contributor?post=309"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp02\/wp-json\/wp\/v2\/license?post=309"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}