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 , there is a vector valued,
-continuous measure of finite variation which has no derivative with respect to
, but which has the property that the closure of its range is compact and convex.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1972-0296248-2
Keywords:
Vector measure,
derivative of a vector measure,
range of a vector measure,
Radon-Nikodym property
Article copyright:
© Copyright 1972
American Mathematical Society