Episode Details

MIT 18.100B Real Analysis, Spring 2025
Instructor: Tobias Holck Colding
View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG

We will show that continuous functions are integrable. This means that the graph of such a function bound a well defined area. To do so, we define what it means for a function to be uniformly continuous. This is a strong version of continuity but we will see that all continuous functions on a closed and bounded interval have this stronger property. Once we have shown that all continuous functions on a compact interval are uniformly continuous, it will follow relatively easily that they are integrable.

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