Almost Everywhere First-Return Recovery

Volume 52 / 2004

Michael J. Evans, Paul D. Humke Bulletin Polish Acad. Sci. Math. 52 (2004), 185-195 MSC: Primary 28A20, 26A42. DOI: 10.4064/ba52-2-9


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.


  • Michael J. EvansDepartment of Mathematics
    Washington and Lee University
    Lexington, VA 24450, U.S.A.
  • Paul D. HumkeDepartment of Mathematics
    St. Olaf College
    Northfield, MN 45701, U.S.A.

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