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

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2024年4月25日

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Szymon Głąb,
Mateusz Lichman,
Michał Pawlikowski

摘要

Recently Tomasz Natkaniec in (Natkaniec in Rev R Acad Cenc Exactas Fís Nat Ser A Mat RACSAM, 115(1):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 $2^\mathfrak c$ $2^{c}$ many generators.