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Lebesgue's Theorem on Riemann Integration
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How nice does a function have to be to be integrable? I'm glad you asked! So long as the function is not too discontinuous, we're in the clear. But what exactly does that mean? If the set of discontinuities of a function, extended to all of n dimensional Euclidean space, has Lebesgue measure zero, then the function in question is integrable.
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