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arXiv · 2309.00830

On strong algebrability of families of non-measurable functions of two variables

Szymon Głcab·Mateusz Lichman·Michał Pawlikowski
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Abstract

Recently Tomasz Natkaniec in [On lineability of families of non-measurable functions of two variable. Rev. R. Acad. Cienc. Exactas F\'is. Nat. Ser. A Mat. RACSAM, 115(1):Paper No. 33, 10, 2021] studied the lineability problem for several classes of non-measurable functions in two variables. In this note we improve his results in the direction of algebrability. In particular, we show that most of the classes considered by Natkaniec contain free algebras with $2^{\mathfrak{c}}$ many generators.

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Szymon Głcab, Mateusz Lichman, Michał Pawlikowski. 2023-09-02. On strong algebrability of families of non-measurable functions of two variables. https://arxiv.org/abs/2309.00830

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