Uniform distribution on locally compact groups
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- by Harald Rindler PDF
- Proc. Amer. Math. Soc. 57 (1976), 130-132 Request permission
Abstract:
In this paper we give a short proof of the existence of uniformly distributed sequences in separable locally compact groups, a result first stated by Benzinger [1]. The existence of u.d. sequences in separable compact groups was proved by Veech [7] whose results also imply the above result. We also prove the existence of well-distributed sequences.References
- Leonora Benzinger, Uniformly distributed sequences in locally compact groups. I, II, Trans. Amer. Math. Soc. 188 (1974), 149–165; ibid. 188 (1974), 167-178. MR 333063, DOI 10.1090/S0002-9947-1974-0333063-1
- I. D. Berg, M. Rajagopalan, and L. A. Rubel, Uniform distribution in locally compact Abelian groups, Trans. Amer. Math. Soc. 133 (1968), 435–446. MR 227695, DOI 10.1090/S0002-9947-1968-0227695-6
- Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549
- Siegfried Grosser and Martin Moskowitz, Compactness conditions in topological groups, J. Reine Angew. Math. 246 (1971), 1–40. MR 284541, DOI 10.1515/crll.1971.246.1
- Herbert Heyer, Dualität lokalkompakter Gruppen, Lecture Notes in Mathematics, Vol. 150, Springer-Verlag, Berlin-New York, 1970 (German). MR 0274648
- L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. MR 0419394
- William A. Veech, Some questions of uniform distribution, Ann. of Math. (2) 94 (1971), 125–138. MR 286980, DOI 10.2307/1970738
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 130-132
- MSC: Primary 22D99; Secondary 10K05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0417094-6
- MathSciNet review: 0417094