On the Semicontinuity in Product Spaces

Details On the Semicontinuity in Product Spaces On the Semicontinuity in Product Spaces

2002-01-23

arxiv.org/abs/math/0201222v1

Mathematics

General Topology

8 pages Latex

Scientific paper

Let $X,Y$ be topological vector spaces or metric spaces, and let {$f:X\times Y \to \Re $} be a real function lower semicontinuous in the first variable and upper semicontinuous in the second one. It is proved that $f$ is globally measurable. Sierpinski (1925) has been raised this question in the case $X=Y=\Re $. This particular case was solved by Kempisty (1929). The actual result has applications in Calculus of Variations.

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