If $f$ and $g$ are functions defined in a normed space, where $f$ and $g$ are weakly lower semicontinuous. What I can say about $ G(x) = (f - g)(x)$?
Are there hypothesis, which can ensure that $G$ is w.l.s.c?
2026-04-08 14:09:59.1775657399
Is the difference of two functions weakly lower semicontinuous a function w.l.s.c?
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When $f=0$ $f-g$ is u.s.c. and when $g=0$ it is l.s.c.. There are no natural conditions under which $f-g$ is l.s.c. or u.s.c..