**
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE **

Vol. LXXII, 2 (2003)

p. 261 – 278

"More or Less" First-return Recoverable Functions

P. D. Humke and M. J. Evans

**Abstract**.
It is known that a real-valued function defined on the unit
interval is first-return recoverable if and only if itbelongs to
Baire class one. Further, it is known that if first-return
recoverability is replaced by stronger notions, such as universal
or consistent first-return recoverability, then familiar
subclasses of the Baire one functions are obtained. Likewise, if
first-return recoverability is weakened to first-return
recoverability except on a set of measure zero [first category],
then one obtains precisely the class of Lebesgue measurable
functions [functions having the Baire property]. Here we examine
the situation where even smaller exceptional sets (countable or
scattered) are excluded, and then explore possibility of combining
these various methods for strengthening and weakening
recoverability.

**AMS subject classification**:
26A21; **Secondary**: 26A15

**Keywords**:
First-return recoverability, Baire one functions

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Acta Mathematica Universitatis Comenianae

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