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arXiv · 1506.01068

Classification of bounded Baire class $ξ$ functions

Viktor Kiss
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Abstract

Kechris and Louveau showed that each real-valued bounded Baire class 1 function defined on a compact metric space can be written as an alternating sum of a decreasing countable transfinite sequence of upper semi-continuous functions. Moreover, the length of the shortest such sequence is essentially the same as the value of certain natural ranks they defined on the Baire class 1 functions. They also introduced the notion of pseudouniform convergence to generate some classes of bounded Baire class 1 functions from others. The main aim of this paper is to generalize their results to Baire class $ξ$ functions. For our proofs to go through, it was essential to first obtain similar results for Baire class 1 functions defined on not necessary compact Polish spaces. Using these new classifications of bounded Baire class $ξ$ functions, one can define natural ranks on these classes. We show that these ranks essentially coincide with those defined by Elekes et. al.

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Viktor Kiss. 2016-01-25. Classification of bounded Baire class $ξ$ functions. https://doi.org/10.4064/fm194-1-2016

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