{"id":305,"date":"2026-09-21T14:07:19","date_gmt":"2026-09-21T11:07:19","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/benli\/?page_id=305"},"modified":"2026-10-15T14:38:36","modified_gmt":"2026-10-15T11:38:36","slug":"math-419-measure-theory-fall-2026","status":"publish","type":"page","link":"https:\/\/blog.metu.edu.tr\/benli\/teaching\/math-419-measure-theory-fall-2026\/","title":{"rendered":"Math 419 Measure Theory Fall 2026"},"content":{"rendered":"<p>Hello, I will (try to) keep a list of topics we have covered each week here:<\/p>\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-6730d294-aded-420c-bfba-c035d08b4985\" href=\"https:\/\/blog.metu.edu.tr\/benli\/files\/2026\/10\/MATH-419-Fall-2026.pdf\">MATH 419-Fall 2026-Syllabus<br><\/a><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Week 1:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We have seen that it is not possible to measure all subsets of R^n.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Recalled Riemann integration and shortcomings of the Riemann Integral.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Defined sigma algebras and measure spaces. Proved simple properties of measures.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Week 2<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Defined the outer measure on R^n and explored its properties.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Week 3<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Defined measurable subsets and the Lebesgue measure. Proved that measurable subsets differ from <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">open subsets by arbitrary small measure.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hello, I will (try to) keep a list of topics we have covered each week here: Week 1: We have seen that it is not possible to measure all subsets of R^n. Recalled Riemann integration and shortcomings of the Riemann Integral. Defined sigma algebras and measure spaces. Proved simple properties of measures. Week 2 Defined [&hellip;]<\/p>\n","protected":false},"author":4219,"featured_media":0,"parent":7,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-305","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/benli\/wp-json\/wp\/v2\/pages\/305","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/benli\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/benli\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/benli\/wp-json\/wp\/v2\/users\/4219"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/benli\/wp-json\/wp\/v2\/comments?post=305"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/benli\/wp-json\/wp\/v2\/pages\/305\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/benli\/wp-json\/wp\/v2\/pages\/7"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/benli\/wp-json\/wp\/v2\/media?parent=305"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}