Uniformly exhaustive submeasures and nearly additive set functions

Authors:
N. J. Kalton and James W. Roberts

Journal:
Trans. Amer. Math. Soc. **278** (1983), 803-816

MSC:
Primary 28A60; Secondary 46A06

MathSciNet review:
701524

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Abstract: Every uniformly exhaustive submeasure is equivalent to a measure. From this, we deduce that every vector measure with compact range in an -space has a control measure. We also show that (or any -space) is a -space, i.e. cannot be realized as the quotient of a nonlocally convex -space by a one-dimensional subspace.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1983-0701524-4

Keywords:
Submeasures,
control measure,
twisted sum

Article copyright:
© Copyright 1983
American Mathematical Society