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arXiv · 1107.1510

Problem with almost everywhere equality

Piotr Niemiec
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Abstract

A topological space $Y$ is said to have (AEEP) if the following condition is fulfilled. Whenever $(X,\mathfrak{M})$ is a measurable space and $f, g: X \to Y$ are two measurable functions, then the set $Δ(f,g) = \{x \in X:\ f(x) = g(x)\}$ is a member of $\mathfrak{M}$. It is shown that a metrizable space $Y$ has (AEEP) iff the cardinality of $Y$ is no greater than $2^{\aleph_0}$.

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Piotr Niemiec. 2011-07-07. Problem with almost everywhere equality. https://doi.org/10.4064/ap104-1-8

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