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


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Article Info

DATE

1987-05

AUTHORS

Robert F. Tichy

ABSTRACT

LetX be a compact metric space, le μ be a non-negative normalized Borel measure onX and letf be a measurable bounded real-valued function defined onX such thatf is μ-almost everywhere continuous and different from zero. It is proved that a sequence (xn),n=1,2, … of points inX is μ-uniformly distributed if and only if for every Borel setE⊆X with μ(Bd(E))=0 we have where 1E denotes the characteristic function ofE andbdE the boundary ofE. Furthermore some quantitative aspects and generalizations of this theorem are discussed. More... »

PAGES

332-342

References to SciGraph publications

  • 1916-09. Über die Gleichverteilung von Zahlen mod. Eins in MATHEMATISCHE ANNALEN
  • 1950. Measure Theory in NONE
  • 1955-01. Zur formalen Theorie der Gleichverteilung in kompakten Gruppen in RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO SERIES 2
  • 1956-03. Folgen auf kompakten Räumen in ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITÄT HAMBURG
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    http://scigraph.springernature.com/pub.10.1007/bf02843743

    DOI

    http://dx.doi.org/10.1007/bf02843743

    DIMENSIONS

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