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REPRESENTATIONS OF WEAK AND STRONG INTEGRALS IN BANACH SPACES

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 represen...

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Pubblicato in:Proc Natl Acad Sci U S A
Autore principale: Brooks, James K.
Natura: Artigo
Lingua:Inglês
Pubblicazione: National Academy of Sciences 1969
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Accesso online:https://ncbi.nlm.nih.govhttps://pmc.ncbi.nlm.nih.gov/articles/PMC223557/
https://ncbi.nlm.nih.govhttps://pubmed.ncbi.nlm.nih.gov/16591755/
https://ncbi.nlm.nih.govhttps://doi.org/10.1073/pnas.63.2.266
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