Uniformly Exhaustive Submeasures and Nearly Additive Set Functions
Authors:
- N. J. KaltonNKN. J. Kalton
- James W. RobertsJRJames W. Roberts
- 1 August 1983
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 278 (2) , 803-816
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.
Keywords
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