A vector measure with no derivative
Author:
D. R. Lewis
Journal:
Proc. Amer. Math. Soc. 32 (1972), 535-536
MSC:
Primary 28A45
DOI:
https://doi.org/10.1090/S0002-9939-1972-0296248-2
MathSciNet review:
0296248
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Abstract | References | Similar Articles | Additional Information
Abstract: Given a nonatomic scalar measure $\mu$, there is a vector valued, $\mu$-continuous measure of finite variation which has no derivative with respect to $\mu$, but which has the property that the closure of its range is compact and convex.
- C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164. MR 115069, DOI https://doi.org/10.4064/sm-17-2-151-164
- Nelson Dunford and B. J. Pettis, Linear operations on summable functions, Trans. Amer. Math. Soc. 47 (1940), 323–392. MR 2020, DOI https://doi.org/10.1090/S0002-9947-1940-0002020-4
- A. Pełczyński, Banach spaces on which every unconditionally converging operator is weakly compact, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 641–648. MR 149295 D. R. Lewis and C. Stegall, Banach spaces whose duals are isomorphic to ${l_1}(\Gamma )$ (submitted).
- J. J. Uhl Jr., The range of a vector-valued measure, Proc. Amer. Math. Soc. 23 (1969), 158–163. MR 264029, DOI https://doi.org/10.1090/S0002-9939-1969-0264029-1
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Additional Information
Keywords:
Vector measure,
derivative of a vector measure,
range of a vector measure,
Radon-Nikodym property
Article copyright:
© Copyright 1972
American Mathematical Society
