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On the Pettis measurability theorem

Published online by Cambridge University Press:  17 April 2009

Dietrich Helmer
Dietrich Helmer
Affiliation:
Department of MathematicsUniversity of BahrainPO Box 32038 Isa Town, Bahrain
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Abstract

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It is shown that, in Pettis's criterion for Bochner measurability of a vector-valued function f: S → X, scalar measurability of f can be weakened to requiring that u of be measurable for u in some subset of the dual X* separating the points of X. Even then, the separability hypotheses in Pettis's Theorem can be weakened as well.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 1 , August 1994 , pp. 109 - 116
Copyright
Copyright © Australian Mathematical Society 1994

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