Weak convergence and weak compactness in the space of integrable functions with respect to a vector meansure
Keywords:Weak convergence, Weak compactness, Integrable functions, Measure and integration
We consider weak convergence and weak compactness in the space L1(m) of real valued integrable functions with respect to a Banach space calued measure m equipped with its natural norm. We give necessary and sufficient conditions for a sequence in L1(m) to be weak Cauchy, and we give necessary and sufficient conditions for a subset of L1(m) to be conditionally sequentially weakly compact.
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