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