MIT 18.102 Introduction to Functional Analysis, Spring 2021 - Lecture 7: Sigma Algebras

MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=OHiu2F18dFA&list=PLUl4u3cNGP63micsJp_--fRAjZXPrQzW_&index=7 Last time, we introduced outer measures, which have most properties we want for a measure. We define Lebesgue measurable sets and ultimately the Lebesgue measure. We also define sigma-algebras, including the important Borel sigma-algebra. License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu Support OCW at http://ow.ly/a1If50zVRlQ We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.