A new proof for the Banach-Zarecki theorem: A light on integrability and continuity
Mathematical Physics
2012-06-13 v1 math.MP
Abstract
To demonstrate more visibly the close relation between the continuity and integrability, a new proof for the Banach-Zarecki theorem is presented on the basis of the Radon-Nikodym theorem which emphasizes on measure-type properties of the Lebesgue integral. The Banach-Zarecki theorem says that a real-valued function F is absolutely continuous on a finite closed interval if and only if it is continuous and of bounded variation when it satisfies Lusin's condition (N).
Keywords
Cite
@article{arxiv.1206.2602,
title = {A new proof for the Banach-Zarecki theorem: A light on integrability and continuity},
author = {Ali Mahdipour-Shirayeh and Homayoon Eshraghi},
journal= {arXiv preprint arXiv:1206.2602},
year = {2012}
}
Comments
15 pages; Published in the Bulletin of Iranian Mathematical Society, 2012