Measures on Hyperspaces

Author

W. J. Charatonik, Missouri University of Science and TechnologyFollow
Matt Insall, Missouri University of Science and TechnologyFollow

Abstract

From a measure space, (X, μ^𝕏) 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 μ^𝕏 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, μ^ℙ(𝕏) is always supported on the hyperspace of finite subsets.

Recommended Citation

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

Department(s)

Mathematics and Statistics

Keywords and Phrases

Hyperspace; Measure; Topological space

International Standard Serial Number (ISSN)

0002-9939; 1088-6826

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2016 American Mathematical Society, All rights reserved.

Publication Date

01 Nov 2016