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Title

On Pettis integral and Radon measures

Authors 1

Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Kopernika 18, 51-617 Wrocław, Poland

Abstract

Assuming the continuum hypothesis, we construct a universally weakly measurable function from [0,1] into a dual of some weakly compactly generated Banach space, which is not Pettis integrable. This (partially) solves a problem posed by Riddle, Saab and Uhl [13]. We prove two results related to Pettis integration in dual Banach spaces. We also contribute to the problem whether it is consistent that every bounded function which is weakly measurable with respect to some Radon measure is Pettis integrable.

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Fundamenta Mathematicae
1998/156/2
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Pages:
183-195
Main language of publication
English
Received
1997-06-24
Accepted
1997-09-22
Published
1998
Exact and natural sciences