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arXiv · 2006.03867

A Remark on Lebesgue Criterion

Yu-Lin Chou
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Abstract

We remark a variant of the existence part of the fundamental theorem of calculus, which, together with the Lebesgue differentiation theorem, constitute a new proof that every Riemann-integrable function on a compact interval having limit everywhere on the interior is almost everywhere continuous with respect to Lebesgue measure. The proof is intended as a new connection between Lebesgue differentiation theorem and Lebesgue criterion of Riemann integrability.

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Yu-Lin Chou. 2020-06-06. A Remark on Lebesgue Criterion. https://arxiv.org/abs/2006.03867

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