A note on the Radon-Nikodym theorem
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- by Tae Geun Cho and A. Tong PDF
- Proc. Amer. Math. Soc. 39 (1973), 530-534 Request permission
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.References
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- M. A. Rieffel, The Radon-Nikodym theorem for the Bochner integral, Trans. Amer. Math. Soc. 131 (1968), 466–487. MR 222245, DOI 10.1090/S0002-9947-1968-0222245-2
- J. J. Uhl Jr., The range of a vector-valued measure, Proc. Amer. Math. Soc. 23 (1969), 158–163. MR 264029, DOI 10.1090/S0002-9939-1969-0264029-1
Additional Information
- © Copyright 1973 American Mathematical Society
- 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