Abstract
Let (μn) be a sequence of probability measures on a discrete semigroup S. In this paper we study the (left, right) uniform distribution of (μn), i.e. the vague or norm convergence of μn−δxμn→0 for every x in S δx means the point measure of x and δxμn the convolution of δx and μn). We shall give equivalent conditions for the (left, right) uniform distributed sequences and relate the existence of such sequences to the (left, right) amenable semigroups. In the last section we consider especially the uniform distribution of the convolution sequence μn of a probability measure.
Similar content being viewed by others
Literatur
Bhattacharya, R.N.,Speed of Convergence of the n-Fold Convolution of a Probability measure on a Compact Group, Z. Wahrscheinlichkeitstheorie verw. Geb. 25 (1972/73), 1–10.
Day, M.M.,Amenable Semigroups, Illionios J. Math. 1 (1957), 509–544.
Gerl, P.,Gleichverteilung auf lokalkompakten Gruppen, Math. Nachr. 71 (1976), 249–260.
Kerstan, J. und K. Matthes,Gleichverteilungseigenschaften von Faltungen von Verteilungsgesetzen auf lokalkompakten abelschen Gruppen. I, Math. Nachr. 37 (1968), 267–312.
Kinzl, F.,Ein Null-Zwei-Gesetz auf Abelschen Halbgruppen, Sitzungsberichte Österr. Akad. Wiss. Mathem.-naturw. K1. Abt. II, 185 (1976), 377–385.
Kuipers, L. and H. Hiederreiter,Uniform distribution of sequences, New York-London-Syndney-Toronto: John Wiley & Sons 1974.
Maxones, W. und H. Rindler,Bemerkungen zu einer Arbeit von P. Ger1:Gleichverteilung auf lokalkompakten Gruppen, Math. Nachr. 41 (1977), 175–184.
Per Martin-Löf,Probability Theory on Discrete Semigroups, Z. Wahrscheinlichkeitstheorie verw. Geb. 4 (1965), 78–102.
Author information
Authors and Affiliations
Additional information
Communicated by K. Keimel
Rights and permissions
About this article
Cite this article
Kinzl, F. Gleichverteilung auf Diskreten Halbgruppen. Semigroup Forum 18, 105–118 (1979). https://doi.org/10.1007/BF02574181
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02574181