Only trivial Borel measures on S_∞ are quasi-invariant under automorphisms

Robert Richard Kallman

Vol. 76 (1978), No. 2, 453–461

DOI: 10.2140/pjm.1978.76.453

Abstract

Let S_∞ be the group of all permutations of the integers. Then the only σ-finite Borel measures on S_∞ which are quasi-invariant under automorphisms are supported on the finite permutations.

Mathematical Subject Classification 2000

Primary: 28A70, 28A70

Secondary: 22A10

Milestones

Received: 23 July 1976

Revised: 20 July 1977

Published: 1 June 1978