On the Semicontinuity in Product Spaces
Antonio J. B. Lopes-Pinto, Diana Aldea Mendes
Abstract
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.
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