Finitely additive measures on groups and rings

  • Sophie Frisch
  • Milan Paštéka
  • Robert F. Tichy
  • Reinhard Winkler


On topological groups a natural finitely additive measure can be defined via compactifications. It is closely related to Hartman's concept of uniform distribution on non-compact groups (cf. [3]). Applications to several situations are possible. Some results of M. Paštéka and other authors on uniform distribution with respect to translation invariant finitely additive probability measures on Dedekind domains are transferred to more general situations. Furthermore it is shown that the range of a polynomial of degree ≥2 on a ring of algebraic integers has measure 0.


Haar Measure Finite Index Ideal Measure Algebraic Integer Dedekind Domain 
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Copyright information

© Springer 1999

Authors and Affiliations

  • Sophie Frisch
    • 1
  • Milan Paštéka
    • 2
  • Robert F. Tichy
    • 1
  • Reinhard Winkler
    • 3
    • 4
  1. 1.Institut für MathematikTU GrazGrazAustria
  2. 2.Faculty of SciencesUniversity of OstravaOstravaCzech Republic
  3. 3.Institut für Algebra und ComputermathematikTU WienWienAustria
  4. 4.Institut für Diskrete MathematikAustrian Academy of SciencesWienAustria

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