Generalized Baire class functions

2024/11/26 by LUCA MOTTO ROS, Ros, Luca Motto, BEATRICE PITTON +1 · 1 citation
#FOS: Mathematics #Logic (math.LO) #Primary: 03E15 #Secondary: 54E99

paper · doi:10.48550/arxiv.2411.17650

Abstract

Let λ be an uncountable cardinal such that 2^{< λ} = λ. Working in the setup of generalized descriptive set theory, we study the structure of λ⁺-Borel measurable functions with respect to various kinds of limits, and isolate a suitable notion of λ-Baire class ξ function. Among other results, we provide higher analogues of two classical theorems of Lebesgue, Hausdorff, and Banach, namely: (1) A function is λ⁺-Borel measurable if and only if it can be obtained from continuous functions by iteratively applying pointwise D-limits, where D varies among directed sets of size at most λ. (2) A function is of λ-Baire class ξ if and only if it is \boldsymbolΣ⁰_ξ+1-measurable.

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