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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Veröffentlicht in:	Proceedings of the National Academy of Sciences - PNAS 1969-06, Vol.63 (2), p.266-270
1. Verfasser:	Brooks, James K.
Format:	Artikel
Sprache:	eng
Schlagworte:	Banach space Integrable functions Mathematical functions Mathematical integrals Mathematical integration Mathematical theorems Mathematical vectors Perceptron convergence procedure Physical Sciences: Mathematics Series convergence
Online-Zugang:	Volltext
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