no. 2
A note on almost strong liftings
Annales de l'Institut Fourier, Tome 21 (1971) no. 2, pp. 35-41.

Soit X un espace localement compact. Un relèvement ρ de M R ∞ (X,μ), où μ est une mesure positive sur X, est presque fort si pour toute fonction continue et bornée f, ρ(f) et f coïncident localement μ-presque partout. On démontre ici que l’ensemble des mesures μ sur X telles qu’il existe un relèvement presque fort de M R ∞ (X,|μ|), est une bande.

Let X be a locally compact space. A lifting ρ of M R ∞ (X,μ) where μ is a positive measure on X, is almost strong if for each bounded, continuous function f, ρ(f) and f coincide locally almost everywhere. We prove here that the set of all measures μ on X such that there exists an almost strong lifting of M R ∞ (X,|μ|) is a band.

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     title = {A note on almost strong liftings},
     journal = {Annales de l'Institut Fourier},
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     publisher = {Institut Fourier},
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Ionescu-Tulcea, C.; Maher, R. A note on almost strong liftings. Annales de l'Institut Fourier, Tome 21 (1971) no. 2, pp. 35-41. doi : 10.5802/aif.372. https://aif.centre-mersenne.org/articles/10.5802/aif.372/

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[5] A. Ionescu Tulcea and C. Ionescu Tulcea, On the lifting property, (IV). Disintegration of measures, Ann. Inst. Fourier, 14, 445-472 (1964). | Numdam | Zbl

[6] A. Ionescu Tulcea and C. Ionescu Tulcea, On the existence of a lifting commuting with the left translations of an arbitrary locally compact group, Proceedings Fifth Berkeley Symposium on Math. Stat. and Probability, Univ. of California Press (1967). | MR | Zbl

[7] A. Ionescu Tulcea and C. Ionescu Tulcea, Topics in the theory of lifting, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 48 (1969), Springer-Verlag, Berlin. | MR | Zbl

[8] R. Maher, A note on strong liftings, J. Math. Anal. and Appl., 29, 633-639 (1970). | MR | Zbl

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