A criterion for the uniform distribution of sequences in compact metric spaces

Robert F. Tichy*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let X be a compact metric space, le μ be a non-negative normalized Borel measure on X and let f be a measurable bounded real-valued function defined on X such that f is μ-almost everywhere continuous and different from zero. It is proved that a sequence (x n ), n=1,2, ... of points in X is μ-uniformly distributed if and only if for every Borel set E⊆X with μ(Bd(E))=0 we have {Mathematical expression} where 1 E denotes the characteristic function of E and bdE the boundary of E. Furthermore some quantitative aspects and generalizations of this theorem are discussed.

Original languageEnglish
Pages (from-to)332-342
Number of pages11
JournalRendiconti del Circolo Matematico di Palermo
Volume36
Issue number2
DOIs
Publication statusPublished - 1 May 1987
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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