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 v0 be a Radon measure on Y = X/G, and let μ be the Haar lift of v0. Let ρ0 be a strong lifting of M∞(Y, v0). We will show that M∞(X, μ) admits a strong lifting ρ which extends ρ0 and commutes with G.

Existence of a strong lifting commuting with a compact group of transformations II / R. Johnson. - In: PACIFIC JOURNAL OF MATHEMATICS. - ISSN 0030-8730. - STAMPA. - 82:(1979), pp. 457-461. [10.2140/pjm.1979.82.457]

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

JOHNSON, RUSSELL ALLAN
1979

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 v0 be a Radon measure on Y = X/G, and let μ be the Haar lift of v0. Let ρ0 be a strong lifting of M∞(Y, v0). We will show that M∞(X, μ) admits a strong lifting ρ which extends ρ0 and commutes with G.
1979
82
457
461
R. Johnson
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/396069
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