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.

@article{AIF_1971__21_2_35_0,
     author = {Ionescu-Tulcea, C. and Maher, R.},
     title = {A note on almost strong liftings},
     journal = {Annales de l'Institut Fourier},
     pages = {35--41},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {21},
     number = {2},
     year = {1971},
     doi = {10.5802/aif.372},
     mrnumber = {48 #9393},
     zbl = {0205.42201},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.372/}
}
TY  - JOUR
AU  - Ionescu-Tulcea, C.
AU  - Maher, R.
TI  - A note on almost strong liftings
JO  - Annales de l'Institut Fourier
PY  - 1971
SP  - 35
EP  - 41
VL  - 21
IS  - 2
PB  - Institut Fourier
PP  - Grenoble
UR  - http://archive.numdam.org/articles/10.5802/aif.372/
DO  - 10.5802/aif.372
LA  - en
ID  - AIF_1971__21_2_35_0
ER  - 
%0 Journal Article
%A Ionescu-Tulcea, C.
%A Maher, R.
%T A note on almost strong liftings
%J Annales de l'Institut Fourier
%D 1971
%P 35-41
%V 21
%N 2
%I Institut Fourier
%C Grenoble
%U http://archive.numdam.org/articles/10.5802/aif.372/
%R 10.5802/aif.372
%G en
%F 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) no. 2, pp. 35-41. doi : 10.5802/aif.372. http://archive.numdam.org/articles/10.5802/aif.372/

[1] K. Bichteler, An existence theorem for strong liftings, to appear in the J. Math. Anal. and Appl. | Zbl

[2] K. Bichteler, On the strong lifting property, in manuscript. | Zbl

[3] N. Bourbaki, Intégration, Chap. I-IV (1965), and Chap. v (1967), Hermann, Paris.

[4] J. Dieudonné, Sur le théorème de Lebesgue-Nikodym, IV, J. Indian Math. Soc., N.S., 15, 77-86 (1951). | MR | Zbl

[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

Cité par Sources :