Almost Everywhere First-Return Recovery
Volume 52 / 2004
Bulletin Polish Acad. Sci. Math. 52 (2004), 185-195
MSC: Primary 28A20, 26A42.
DOI: 10.4064/ba52-2-9
Abstract
We present a new characterization of Lebesgue measurable functions; namely, a function $f:[0,1]\to {\Bbb R}$ 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.
