The concentration function problem for $G$-spaces

Document Type : Research Paper

Author

Department of Mathematics‎, ‎Tarbiat Modares University‎, ‎Tehran 14115-134‎, ‎Iran.

Abstract

‎In this note‎, ‎we consider the concentration function problem for a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$‎. ‎We prove a necessary and sufficient condition for the concentration functions of a‎ ‎spread-out irreducible probability measure $\mu$ on $G$ to converge to zero.

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References

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S.R. Foguel, More on the zero-two" law, Proc. Amer. Math. Soc. 61 (1976), no. 2, 262--264.
K.H. Hofmann and A. Mukherjea, Concentration functions and a class of noncompact groups, Math. Ann. 256 (1981), no. 4, 535--548.
W. Jaworski, J. Rosenblatt and G. Willis, Concentration functions in locally compact groups, Math. Ann. 305 (1996), no. 4, 673--691.
A. Mukherjea, Limit theorems for probability measures on non-compact groups and semi-groups, Z. Wahrscheinlichkeitstheorie und Verw, Gebiete 33 (1976), no. 4, 273--284.
Bulletin of the Iranian Mathematical Society
Volume 43, Issue 3
June 2017
Pages 763-769

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History

  • Receive Date: 21 December 2015
  • Revise Date: 17 February 2016
  • Accept Date: 17 February 2016

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