Uniform measures and countably additive measures
msra(2007)
摘要
Uniform measures are defined as the functionals on the space of bounded
uniformly continuous functions that are continuous on bounded uniformly
equicontinuous sets. If every cardinal has measure zero then every countably
additive measure is a uniform measure. The functionals sequentially continuous
on bounded uniformly equicontinuous sets are exactly uniform measures on the
separable modification of the underlying uniform space.
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关键词
functional analysis
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