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.