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arXiv · 1508.02902

On measurability of Banach indicatrix

Nikita Evseev
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Abstract

Given two metric measure spaces $X$ and $Y$. Let $f:X\to Y$ be a measurable mapping and $A\subset X$. The Banach indicatrix (multiplicity function) is defined as $N(y,f,A) = \#\{x\in A \mid f(x) = y\}$. We prove measurability of this multiplicity function. The question was also discussed on http://mathoverflow.net/q/206780/15946.

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Nikita Evseev. 2015-08-12. On measurability of Banach indicatrix. https://doi.org/10.4064/cm6881-7-2017

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