MIT 18.102 Introduction to Functional Analysis, Spring 2021 - Lecture 12: Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence...

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=W2pw1JWc9k4&list=PLUl4u3cNGP63micsJp_--fRAjZXPrQzW_&index=12 We define the class of Lebesgue integrable functions and the Lebesgue integral, and we prove the powerful Dominated Convergence Theorem! We conclude by showing that the Riemann and Lebesgue integrals agree for continuous functions on a bounded interval. 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.