A problem with almost everywhere equality
Volume 104 / 2012
Annales Polonici Mathematici 104 (2012), 105-108
MSC: piotr.niemiec@uj.edu.pl
DOI: 10.4064/ap104-1-8
Abstract
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 $2^{\aleph_0}$.
