A note on almost strong liftings

Ionescu-Tulcea, C.; Maher, R.

Annales de l'Institut Fourier, Tome 21 (1971), p. 35-41 / Harvested from Numdam

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Résumé
Abstract

Soit $X$ un espace localement compact. Un relèvement $ρ$ de $M_{R}^{\infty} (X, μ)$ , 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 $M_{R}^{\infty} (X, | μ |)$ , est une bande.

Let $X$ be a locally compact space. A lifting $ρ$ of $M_{R}^{\infty} (X, μ)$ 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 $M_{R}^{\infty} (X, | μ |)$ is a band.

Publié le : 1971-01-01

MR 48 #9393 | Zbl 0205.42201

DOI : https://doi.org/10.5802/aif.372

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     author = {Ionescu-Tulcea, C. and Maher, R.},
     title = {A note on almost strong liftings},
     journal = {Annales de l'Institut Fourier},
     volume = {21},
     year = {1971},
     pages = {35-41},
     doi = {10.5802/aif.372},
     mrnumber = {48 \#9393},
     zbl = {0205.42201},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1971__21_2_35_0}
}

Ionescu-Tulcea, C.; Maher, R. A note on almost strong liftings. Annales de l'Institut Fourier, Tome 21 (1971) pp. 35-41. doi : 10.5802/aif.372. http://gdmltest.u-ga.fr/item/AIF_1971__21_2_35_0/

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