Algebrability of non-measurable functions
Published on:
2 September 2023
Primary Category:
Functional Analysis
Paper Authors:
Szymon Głcab,
Mateusz Lichman,
Michał Pawlikowski
Bullets
Key Details
Proves strong algebrability for several families of non-measurable functions
Main tool is constructing explicit examples of functions in these families
Builds on recent work studying lineability of these function classes
Utilizes notions like sup-measurability, separate measurability, and Darboux/Baire functions
Relies on set-theoretic axioms like Continuum Hypothesis or combinatorial cardinal invariants
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AI generated summary
Algebrability of non-measurable functions
This paper studies the existence of large algebraic structures within various classes of non-measurable functions of two variables. The authors prove these families contain free algebras with continuum many generators, improving prior results on lineability. Key techniques involve constructing explicit non-measurable functions with desired properties.
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