Uniform probability
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.
scientific article; zbMATH DE number 4161752