2005-11-16Buch DOI: 10.18452/2706
On the EPI-Compactness of Equi-Lower Semi-Continuous Functions
In this paper we show that equi-lsc. functions from a topological vector space X to the extended reals are epi-compact without assuming the local compactness or the second countablity of the underlying space X. We also show that weakly equi-lower semicontinuous functions from a Banach space X to the extended reals are Mosco-compact. Finally, we apply these results to prove the Mosoc-compactness of families of integral functionals that arise in optimization problems.
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