Almost Everywhere First-Return Recovery

Michael J. Evans, and Paul D. Humke. "Almost Everywhere First-Return Recovery." Bulletin of the Polish Academy of Sciences. Mathematics 52.2 (2004): 185-195. <http://eudml.org/doc/280354>.

@article{MichaelJ2004,
abstract = {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.},
author = {Michael J. Evans, Paul D. Humke},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {Lebesgue measurable functions; trajectory; trajectory first-return yields Lebesgue integral; Baire property of function},
language = {eng},
number = {2},
pages = {185-195},
title = {Almost Everywhere First-Return Recovery},
url = {http://eudml.org/doc/280354},
volume = {52},
year = {2004},
}

TY - JOUR
AU - Michael J. Evans
AU - Paul D. Humke
TI - Almost Everywhere First-Return Recovery
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2004
VL - 52
IS - 2
SP - 185
EP - 195
AB - 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.
LA - eng
KW - Lebesgue measurable functions; trajectory; trajectory first-return yields Lebesgue integral; Baire property of function
UR - http://eudml.org/doc/280354
ER -