A Remark on Lebesgue Criterion
General Mathematics
2020-06-09 v1
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.
Cite
@article{arxiv.2006.03867,
title = {A Remark on Lebesgue Criterion},
author = {Yu-Lin Chou},
journal= {arXiv preprint arXiv:2006.03867},
year = {2020}
}