Lecture 18: Integrable Functions

MIT 18.100B Real Analysis, Spring 2025
Instructor: Tobias Holck Colding
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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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Post from MIT OpenCourseWare on September 02, 2025

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