On measurability of Banach indicatrix

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.

arXiv comment5 pages, some typoes corrected

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