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Almost Everywhere First-Return Recovery

Michael J. EvansPaul D. Humke — 2004

Bulletin of the Polish Academy of Sciences. Mathematics

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.

Two classes of Darboux-like, Baire one functions of two variables

Michael J. EvansPaul D. Humke — 2010

Czechoslovak Mathematical Journal

Among the many characterizations of the class of Baire one, Darboux real-valued functions of one real variable, the 1907 characterization of Young and the 1997 characterization of Agronsky, Ceder, and Pearson are particularly intriguing in that they yield interesting classes of functions when interpreted in the two-variable setting. We examine the relationship between these two subclasses of the real-valued Baire one defined on the unit square.

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