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Proceedings of the American Mathematical Society

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A note on the Radon-Nikodym theorem


Authors: Tae Geun Cho and A. Tong
Journal: Proc. Amer. Math. Soc. 39 (1973), 530-534
MSC: Primary 28A45; Secondary 28A15, 46G10, 47B05
DOI: https://doi.org/10.1090/S0002-9939-1973-0315085-4
MathSciNet review: 0315085
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Abstract: This paper gives a necessary and sufficient condition in order that a bounded linear mapping from $ {L^1}(\mu )$ into a Banach space be compact. It is applied to provide a slightly improved form of the Radon-Nikoydm theorem for vector valued measures and to give a sufficient condition in order that the range of a vector valued measure of bounded variation be compact.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0315085-4
Keywords: Vector valued measure, Bochner kernel, locally compact operator
Article copyright: © Copyright 1973 American Mathematical Society