On the Semicontinuity in Product Spaces

الأصل · EN

Let X,Y be topological vector spaces or metric spaces, and let f:X× Y → 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=. This particular case was solved by Kempisty (1929). The actual result has applications in Calculus of Variations.