On lower semicontinuity of metric upper semicontinuity of Nemytskij set- valued operators (Q1340801)

Let \(\Omega\) be a measure space, \(X\) and \(Y\) two separable \(F\) spaces, and \(F,\Omega\times X\to 2^ Y\) a sup-measurable multifunction. The authors give sufficient conditions under which the lower or upper semi- continuity of \(F\) carries over to the corresponding Nemytskij operator \(N_ F\) between two modular spaces.