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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
DOI: https://doi.org/10.1090/S0002-9947-1983-0701524-4
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 $ F$-space has a control measure. We also show that $ {c_0}$ (or any $ {\mathcal{L}_\infty }$-space) is a $ \mathcal{K}$-space, i.e. cannot be realized as the quotient of a nonlocally convex $ F$-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

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