# 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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Main Subjects

#### References

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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.

### History

• Receive Date: 21 December 2015
• Revise Date: 17 February 2016
• Accept Date: 17 February 2016
• First Publish Date: 01 June 2017