Geodesic
A problem with almost everywhere equality
Piotr Niemiec1
1Institute of Mathematics Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland
Annales Polonici Mathematici, Tome 104 (2012) no. 1, pp. 105-108

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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 $2^{\aleph_0}$.
DOI : 10.4064/ap104-1-8
Keywords: topological space said have aeep following condition satisfied whenever mathfrak measurable space colon measurable functions set vardelta colon member mathfrak shown metrizable space has aeep cardinality greater nbsp aleph

Piotr Niemiec  1

1 Institute of Mathematics Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland 
Piotr Niemiec. A problem with almost everywhere equality. Annales Polonici Mathematici, Tome 104 (2012) no. 1, pp. 105-108. doi: 10.4064/ap104-1-8
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