Annali di Matematica Pura ed Applicata

, Volume 162, Issue 1, pp 23–32 | Cite as

λ-Equidistributed sequences of partitions and a theorem of the De Bruijn-Post type

  • Franco Chersi
  • Aljoša Volčič
Article
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Summary

The notion of uniform distribution of a sequence is generalized to sequences of partitions in a separable metric space X. Results concern Riemann integrability with respect to a probability λ on X, and Riemann approximations of Lebesgue integrals.

Keywords

Uniform Distribution Result Concern Riemann Integrability Riemann Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. [1]
    N. G. De Brujin -K. A. Post,A remark on uniformly distributed sequences and Riemann integrability, Indag. Math.,30 (1968), pp. 149–150.Google Scholar
  2. [2]
    J.Dugundji,Topology, Allyn and Bacon Inc. (1966).Google Scholar
  3. [3]
    E. Hlawka,The Theory of Uniform Distribution, AB Academic Publishers, Berkhamsted (1984).Google Scholar
  4. [4]
    K.Jacobs,Measure and Integral, Academic Press (1978).Google Scholar
  5. [5]
    S.Kakutani,A problem of equidistribution on the unit interval, in:Measure Theory, Oberwolfach (1975), pp. 369–375; Lect. Notes in Math.,541, Springer-Verlag (1976).Google Scholar
  6. [6]
    L.Kuipers - H.Niederreiter,Uniform Distribution of Sequences, J. Wiley (1974).Google Scholar
  7. [7]
    K. Schmidt,Über einen Zusammenhang zwischen gleichverteilten Punkt- and Massfolgen, J. Reine Angew. Math.,244 (1970), pp. 94–96.Google Scholar
  8. [8]
    L.Schwartz,Radon Measure on Arbitrary Topological Spaces and Cylindrical Measures, Tata Institute of Fundamental Research, Oxford Univ. Press (1973).Google Scholar
  9. [9]
    P. Morales,Mean value theorem for the m-integral of Dinculeanu, Canad. Math. Bull.,15 (2) (1972), pp. 243–251.Google Scholar
  10. [10]
    H. Niederreiter,On the existence of uniformly distributed sequences in compact spaces, Compositio Math.,25 (1972), pp. 93–99.Google Scholar
  11. [11]
    L. R.Parthasarathy,Probability Measures on Metric Spaces, Academic Press (1967).Google Scholar
  12. [12]
    H. Weyl,Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann.,77 (1916, reprint 1964), pp. 313–352.Google Scholar

Copyright information

© Fondazione Annali di Matimatica Pura ed Applicata 1992

Authors and Affiliations

  • Franco Chersi
    • 1
  • Aljoša Volčič
    • 1
  1. 1.Dipartimento di Scienze MatematicheUniversità di TriesteTrieste

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