Weak compactness in the space of vector-valued measures of bounded variation. (English) Zbl 0817.46029
Summary: Let \(X\) be a Banach space and \((\Omega, \Sigma)\) a measure space. A characterization of relatively weak compact subset of the space of \(X\)- valued countably additive vector measures of bounded variation defined on \(\Sigma\) is given.
MSC:
| 46E27 | Spaces of measures |
| 46A50 | Compactness in topological linear spaces; angelic spaces, etc. |
| 46E40 | Spaces of vector- and operator-valued functions |
| 46G10 | Vector-valued measures and integration |
| 28B05 | Vector-valued set functions, measures and integrals |
| 28B20 | Set-valued set functions and measures; integration of set-valued functions; measurable selections |
Keywords:
measure space; relatively weak compact subset of the space of \(X\)-valued countably additive vector measures of bounded variationReferences:
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