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.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.