Continuous Probability Distributions over Second-Countable Spaces are Perfectly Supported

Yu-Lin Chou

No 8zkwt, OSF Preprints from Center for Open Science

Abstract: We prove that every Borel probability measure over an arbitrary second-countable space vanishing at any singletons has support being a perfect set. Thus the support of a continuous probability distribution over a second-countable space turns out to admit a richer structure.

Date: 2021-01-19
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Persistent link: https://EconPapers.repec.org/RePEc:osf:osfxxx:8zkwt

DOI: 10.31219/osf.io/8zkwt

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