English

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.

Keywords

Cite

@article{arxiv.2006.03867,
  title  = {A Remark on Lebesgue Criterion},
  author = {Yu-Lin Chou},
  journal= {arXiv preprint arXiv:2006.03867},
  year   = {2020}
}
R2 v1 2026-06-23T16:06:41.938Z