Uniformly exhaustive submeasures and nearly additive set functions

Kalton, N. J.; Roberts, James W.

doi:10.1090/S0002-9947-1983-0701524-4

Uniformly exhaustive submeasures and nearly additive set functions
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by N. J. Kalton and James W. Roberts

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

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

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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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