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Construction of Regular Non-Atomic Strictly-Positive Measures in Second-Countable Locally Compact Non-Atomic Hausdorff Spaces. (arXiv:1807.05437v1 [math.FA])
来源于:arXiv
This paper presents a constructive proof of the existence of a regular
non-atomic strictly-positive measure on any second-countable locally compact
non-atomic Hausdorff space. This construction involves a sequence of
finitely-additive set functions defined recursively on an ascending sequence of
rings of subsets with a premeasure limit that is extendable to a measure with
the desired properties. Non-atomicity of the space provides a meticulous way to
ensure that the limit is a premeasure. 查看全文>>