Monatshefte für Mathematik

, Volume 121, Issue 1, pp 79–111

Some remarks on countably determined measures and uniform distribution of sequences

  • Sophocles Mercourakis

DOI: 10.1007/BF01299640

Cite this article as:
Mercourakis, S. Monatshefte für Mathematik (1996) 121: 79. doi:10.1007/BF01299640


Two topics are investigated: countably determined (regular Borel probability) measures on compact Hausdorff spaces, and uniform distribution of sequences regarding mainly this kind of measures. We prove several characterizations of countably determined measures, and apply the results in order to show the existence of a well distributed sequence in the support of a countably determined measure. We also generalize a result of Losert on the existence of uniformly distributed sequences in compact dyadic spaces.

1991 Mathematics Subject Classification

Primary: 28A60Secondary: 11K0628A12

Key words

Countably determined measureuniformly regular measureRiemann intergrable functionJordan measurable setuniformly distributed sequence

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Sophocles Mercourakis
    • 1
  1. 1.Department of MathematicsUniversity of AthensAthensGreece