We present a new characterization of Lebesgue measurable functions; namely, a function f:[0,1]→ ℝ is measurable if and only if it is first-return recoverable almost everywhere. This result is established by demonstrating a connection between almost everywhere first-return recovery and a first-return process for yielding the integral of a measurable function.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-2-9,
author = {Michael J. Evans and Paul D. Humke},
title = {Almost Everywhere First-Return Recovery},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {52},
year = {2004},
pages = {185-195},
zbl = {1102.28002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-2-9}
}
Michael J. Evans; Paul D. Humke. Almost Everywhere First-Return Recovery. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) pp. 185-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-2-9/