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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