Uniform probability
type: Item
instance of: scholarly article
title: Uniform probability
zbMATH Open document ID: 0707.60002
DOI: 10.1007/BF01046100
author: William A. Dembski
published in: Journal of Theoretical Probability
publication date: 1990-01-01T00:00:00Z
review text: Let K be a compact metric space and let \(S_{\epsilon}\) be a maximal \(\epsilon\)-dispersed subset of K, \(\epsilon >0\). A uniform probability on K is defined to be a weak limit of \[ | S_{\epsilon}|^{- 1}\sum_{x\in S_{\epsilon}}\delta_ x,\quad as\quad \epsilon \downarrow 0. \] The author, among others, characterizes compacts where the limit exists and extends the construction to some locally compact sets. Examples and open problem are given, too.
Mathematics Subject Classification ID: 60A10
Mathematics Subject Classification ID: 28A75
zbMATH DE Number: 4161752
zbMATH Keywords: weak convergence
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: capacity dimension
zbMATH Keywords: compact metric space
reviewed by: Rimas Norvaiša
MaRDI profile type: Publication
cites work: Q4135799
cites work: Q5515914
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cites work: Q4405392
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cites work: On the Hausdorff dimension of harmonic measure in higher dimension
full work available at URL: https://doi.org/10.1007/bf01046100
OpenAlex ID: W4245419880
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description: scientific article; zbMATH DE number 4161752