A problem with almost everywhere equality

Volume 104 / 2012

Piotr Niemiec Annales Polonici Mathematici 104 (2012), 105-108 MSC: piotr.niemiec@uj.edu.pl DOI: 10.4064/ap104-1-8


A topological space $Y$ is said to have (AEEP) if the following condition is satisfied: Whenever $(X,\mathfrak M)$ is a measurable space and $f,g\colon X \to Y$ are two measurable functions, then the set $\varDelta(f,g) = \{x \in X\colon f(x) = g(x)\}$ is a member of $\mathfrak M$. It is shown that a metrizable space $Y$ has (AEEP) iff the cardinality of $Y$ is not greater than $2^{\aleph_0}$.


  • Piotr NiemiecInstitute of Mathematics
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland

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