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Almost everywhere first-return recovery

Evans M. J., Humke P. D.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 2

185-195

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.