Vector valued functions equivalent to measurable functions

Author:
J. J. Uhl

Journal:
Proc. Amer. Math. Soc. **68** (1978), 32-36

MSC:
Primary 28A20

MathSciNet review:
0466473

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Abstract: Let *X* be a Banach space with dual and let be a finite measure space. Suppose is weakly measurable. There exists a (norm) measurable such that a.e. for each if and only if each set *A* of positive -measure has a subset *B* of positive -measure such that there is a weakly compact convex subset *K* of *X* with the property that

*B*for each .

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1978-0466473-1

Article copyright:
© Copyright 1978
American Mathematical Society