I made these videos primarily to practice speaking. Speaking is easier when I am familiar with the topic. A secondary purpose is to try to prove Lebesgue's theorem by sorting out what I have learned. The first three videos explain important concepts and the last two videos discuss the two directions of the proof.
Video 1: Riemann-integrable Functions with Infinite Discontinuities
Video 2: Sets of Measure Zero
Video 3: α-Continuity
Video 4: Reverse Direction
Video 5: Forward Direction
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