Games characterizing certain families of functions
Marek Balcerzak, Tomasz Natkaniec, and Piotr Szuca
TL;DR
This paper develops game-theoretic characterizations of Baire 1, Baire measurable, and Lebesgue measurable functions between Polish spaces, extending recent results and introducing new frameworks for understanding these classes.
Contribution
It introduces novel game characterizations for Baire 1 functions and their families, expanding the theoretical understanding of these function classes.
Findings
Game characterizations of Baire 1 functions between Polish spaces
Characterizations for equi-Baire 1 families of functions
Game descriptions of Baire and Lebesgue measurable functions
Abstract
We obtain several game characterizations of Baire 1 functions between Polish spaces X, Y which extends the recent result of V. Kiss. Then we propose similar characterizations for equi-Bare 1 families of functions. Also, using related ideas, we give game characterizations of Baire measurable and Lebesgue measurable functions.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory · Advanced Harmonic Analysis Research