Vol. 82, No. 2, 1979

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

Russell Allan Johnson

Vol. 82 (1979), No. 2, 457–461
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
Authors
Russell Allan Johnson