A note on almost strong liftings

Ionescu-Tulcea, C.; Maher, R.

doi:10.5802/aif.372

Ionescu-Tulcea, C. ; Maher, R.

Annales de l'Institut Fourier, Tome 21 (1971) no. 2, pp. 35-41

Abstract (VO)
Résumé

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.

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.

MR Zbl

DOI : 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},
     pages = {35--41},
     year = {1971},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {21},
     number = {2},
     doi = {10.5802/aif.372},
     mrnumber = {48 #9393},
     zbl = {0205.42201},
     language = {en},
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}

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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

Bibliographie
Cité par

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