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arXiv · 2410.21434

Borel regularity is equivalent to Lusin's theorem and the existence of Borel representatives

Ryan Alvarado·Przemysław Górka·Artur Słabuszewski
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Abstract

In this article, we characterize both Lusin's theorem and the existence of Borel representatives via the regularity properties of the measure in general topological measure spaces. As a corollary, we prove that Borel regularity of the measure is both a necessary and sufficient condition for these results to hold true in metric measure spaces.

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Ryan Alvarado, Przemysław Górka, Artur Słabuszewski. 2024-10-28. Borel regularity is equivalent to Lusin's theorem and the existence of Borel representatives. https://arxiv.org/abs/2410.21434

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