The extension and completion of the universal measure and the dual of the space of measures |
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| Authors: | William H Graves Dennis Sentilles |
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| Institution: | Mathematics Department, Phillips Hall, University of North Carolina, Chapel Hill, North Carolina 27514 USA;Mathematics Department, University of Missouri, Columbia, Missouri 65201 USA |
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| Abstract: | Every vector measure μ factors uniquely by μ = gm ° χ where χ is a universal measure and gm is a linear map continuous on simple functions in the strict topology. The completion of χ describes the dual of the space of measures by uniform closure based on χ-measurable sets and also as the completion of the simple functions in the strict topology. |
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