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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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: 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.


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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