December 2013 On the structure of finite level and $\omega$-decomposable Borel functions
Luca Motto Ros
J. Symbolic Logic 78(4): 1257-1287 (December 2013). DOI: 10.2178/jsl.7804150


We give a full description of the structure under inclusion of all finite level Borel classes of functions, and provide an elementary proof of the well-known fact that not every Borel function can be written as a countable union of $\boldsymbol{\Sigma}^0_\alpha$-measurable functions (for every fixed $1 \leq \alpha < \omega_1$). Moreover, we present some results concerning those Borel functions which are $\omega$-decomposable into continuous functions (also called countably continuous functions in the literature): such results should be viewed as a contribution towards the goal of generalizing a remarkable theorem of Jayne and Rogers to all finite levels, and in fact they allow us to prove some restricted forms of such generalizations. We also analyze finite level Borel functions in terms of composition of simpler functions, and we finally present an application to Banach space theory.


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Luca Motto Ros. "On the structure of finite level and $\omega$-decomposable Borel functions." J. Symbolic Logic 78 (4) 1257 - 1287, December 2013.


Published: December 2013
First available in Project Euclid: 5 January 2014

zbMATH: 1323.03065
MathSciNet: MR3156524
Digital Object Identifier: 10.2178/jsl.7804150

Primary: 03E15 , 26A21 , 46B04 , 46J10 , 54C10 , 54E40 , 54H05

Keywords: Baire class of functions , countably continuous function , decomposable function , Finite level Borel function

Rights: Copyright © 2013 Association for Symbolic Logic


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Vol.78 • No. 4 • December 2013
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