Measures on Hyperspaces
From a measure space, (X, μ𝕏) we define a measure μ ℙ(𝕏) on the power set of X. If (X,τ) is a compactum, whose topology τ is compatible with the measure μ𝕏 on X, then the measure μ ℙ(𝕏) restricts to a natural measure on the hyperspace of closed sets of that given compactum. Surprisingly, under very mild conditions, μℙ(𝕏) is always supported on the hyperspace of finite subsets.
W. J. Charatonik and M. Insall, "Measures on Hyperspaces," Proceedings of the American Mathematical Society, vol. 144, no. 11, pp. 4753-4757, American Mathematical Society, Nov 2016.
The definitive version is available at https://doi.org/10.1090/proc/13215
Mathematics and Statistics
Keywords and Phrases
Hyperspace; Measure; Topological space
International Standard Serial Number (ISSN)
Article - Journal
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01 Nov 2016