Borel sets with countable sections for nonseparable spaces

Holický, Petr

doi:10.1090/S0002-9939-05-08099-8

Borel sets with countable sections for nonseparable spaces
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Proc. Amer. Math. Soc. 134 (2006), 1519-1525 Request permission

Abstract:

We prove that every (extended) Borel subset $E$ of $X\times Y$, where $X$ is a complete metric and $Y$ is Polish, can be covered by countably many extended Borel graphs of mappings from $X$ to $Y$ if the sections $E_x=\{y\in Y:(x,y)\in E\}$, $x\in X$, are countable. This is a nonseparable version of a classical theorem of Luzin and Novikov.

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