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The Riemann Integral was developed as a way to calculate the area under a curve. Then came a function that was impossible to integrate. This dilemma would lead one mathematician, Henri Lebesgue, to invent an entirely new approach. The Lebesgue Theory of Integration was a much better theory of integration and it would ultimately change the way we think about the integral forever.
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Video on the Vitali Set: https://youtu.be/hs3eDa3_DzU
What is a Hilbert Space? https://youtu.be/FFPXm-tuOt8
What is a Banach Space? https://youtu.be/Zjo1ACFm5WI
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Article on the Lebesgue Integral: https://arxiv.org/pdf/2309.08908
Music: Epidemic Sound
Animations created using Manim: https://www.manim.community/
Illustrations and Thumbnails: Christine Kosakowski
This video was sponsored by Brilliant
