Mathematical Notes

, Volume 56, Issue 3, pp 978–983 | Cite as

Uniform distribution, invariant means, and Riemann integrals

  • A. I. Shtern


Uniform Distribution Riemann Integral 
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  1. 1.
    Alan Paterson, Amenability, American Math. Soc., Providence (1988).Google Scholar
  2. 2.
    J. Rosenblatt and Z. Yang, “Functions with a unique mean value,” Illinois J. Math.,34, No. 4, 744–764 (1990).MathSciNetGoogle Scholar
  3. 3.
    J. Dixmier, “Les moyennes invariantes dans les semigroupes et leurs applications,” Acta Sci. Math.,12, 213–227 (1950).MATHMathSciNetGoogle Scholar
  4. 4.
    E. Granirer, “On finite equivalent invariant measures for semigroups of transformations,” Duke. Math. J.,38, No. 2, 395–408 (1971).MATHMathSciNetGoogle Scholar
  5. 5.
    G. G. Lorentz, “A contribution to the theory of divergent sequences,” Acta Math.,80, 167–190 (1948).MathSciNetGoogle Scholar
  6. 6.
    M. Day, “Amenable semigroups,” Illinois Math. J.,1, No. 4, 509–544 (1957).MATHMathSciNetGoogle Scholar
  7. 7.
    P. Greenleaf, Invariant Means on Topological Groups and Their Applications [Russian translation], Mir, Moscow (1973).Google Scholar
  8. 8.
    L. Alaoglu and G. Birkhoff, “General ergodic theorems,” Ann. Math.,41, 293–309 (1940).MathSciNetGoogle Scholar
  9. 9.
    A. A. Tempel'man, Ergodic Theorems on Groups [in Russian], Mokslas, Vil'nyus (1986).Google Scholar
  10. 10.
    L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Interscience, New York (1974).Google Scholar
  11. 11.
    E. Yu. Terekhina, “On subsitution of variables in Riemann integrals,” Vestn. MGU, Ser. Mat., Mekh., No. 3, 78–80 (1985).MATHMathSciNetGoogle Scholar
  12. 12.
    C. J. de la Valle Pussen, A Course in the Analysis of the Infinitely Small [Russian translation], Vol. 1, GTTI, Moscow (1933).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • A. I. Shtern
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityUSSR

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