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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Universal Pettis integrability property


Author: Gunnar F. Stefánsson
Journal: Proc. Amer. Math. Soc. 123 (1995), 1431-1435
MSC: Primary 46G10; Secondary 28B05, 46E40
MathSciNet review: 1277135
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Abstract: Functions into duals and pre-duals of weakly compactly generated spaces (WCG) are studied.

We show that a universally weakly measurable function f into a dual of a WCG has the RS property. Also, for such a function, we sharpen the decomposition obtained by E. M. Bator (1988).

We show that bounded weakly measurable functions into pre-duals of WCG spaces are always Pettis integrable, universally weakly measurable, or not.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1277135-5
PII: S 0002-9939(1995)1277135-5
Keywords: Universally weakly measurable, $ {\text{weak}^ \ast }$ integral, Pettis integral
Article copyright: © Copyright 1995 American Mathematical Society