REPRESENTATIONS OF WEAK AND STRONG INTEGRALS IN BANACH SPACES
AUTOR(ES)
Brooks, James K.
RESUMO
We establish a representation of the Gelfand-Pettis (weak) integral in terms of unconditionally convergent series. Moreover, absolute convergence of the series is a necessary and sufficient condition in order that the weak integral coincide with the Bochner integral. Two applications of the representation are given. The first is a simplified proof of the countable additivity and absolute continuity of the indefinite weak integral. The second application is to probability theory; we characterize the conditional expectation of a weakly integrable function.
ACESSO AO ARTIGO
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