Existence of a strong lifting commuting with a compact group of transformations. II

Russell Allan Johnson

Vol. 82 (1979), No. 2, 457–461

DOI: 10.2140/pjm.1979.82.457

Abstract

Let G be a locally compact group with left Haar measure γ. The well-known “Theorem LCG” of A. and C. Ionescu-Tulcea states that there is a strong lifting of M^∞(G,γ) commuting with left translations. Our purpose here is to prove a generalization of this theorem in case G is compact. Thus let (G,X) be a free left transformation group with X and G compact. Let ν₀ be a Radon measure on Y = X∕G, and let μ be the Haar lift of ν₀. Let ρ₀ be a strong lifting of M^∞(Y,ν₀). We will show that M^∞(X,μ) admits a strong lifting ρ which extends ρ₀ and commutes with G.

Mathematical Subject Classification 2000

Primary: 28A51

Secondary: 22D40, 46G15

Milestones

Received: 13 July 1978

Revised: 11 January 1979

Published: 1 June 1979