Problem with almost everywhere equality

Details Problem with almost everywhere equality Problem with almost everywhere equality

2011-07-07

arxiv.org/abs/1107.1510v1

Ann. Polon. Math. 104 (2012), 105-108

Mathematics

General Topology

4 pages

Scientific paper

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 $\Delta(f,g) = \{x \in X:\ f(x) =
g(x)\}$ 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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