A note on almost strong liftings

C. Ionescu-Tulcea; R. Maher

Annales de l'institut Fourier (1971)

  • Volume: 21, Issue: 2, page 35-41
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Ionescu-Tulcea, C., and Maher, R.. "A note on almost strong liftings." Annales de l'institut Fourier 21.2 (1971): 35-41. <http://eudml.org/doc/74037>.

@article{Ionescu1971,
abstract = {Let $X$ be a locally compact space. A lifting $\rho $ of $M^\infty _R(X,\mu )$ where $\mu $ is a positive measure on $X$, is almost strong if for each bounded, continuous function $f$, $\rho (f)$ and $f$ coincide locally almost everywhere. We prove here that the set of all measures $\mu $ on $X$ such that there exists an almost strong lifting of $M^\infty _R(X,|\mu |)$ is a band.},
author = {Ionescu-Tulcea, C., Maher, R.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {35-41},
publisher = {Association des Annales de l'Institut Fourier},
title = {A note on almost strong liftings},
url = {http://eudml.org/doc/74037},
volume = {21},
year = {1971},
}

TY - JOUR
AU - Ionescu-Tulcea, C.
AU - Maher, R.
TI - A note on almost strong liftings
JO - Annales de l'institut Fourier
PY - 1971
PB - Association des Annales de l'Institut Fourier
VL - 21
IS - 2
SP - 35
EP - 41
AB - Let $X$ be a locally compact space. A lifting $\rho $ of $M^\infty _R(X,\mu )$ where $\mu $ is a positive measure on $X$, is almost strong if for each bounded, continuous function $f$, $\rho (f)$ and $f$ coincide locally almost everywhere. We prove here that the set of all measures $\mu $ on $X$ such that there exists an almost strong lifting of $M^\infty _R(X,|\mu |)$ is a band.
LA - eng
UR - http://eudml.org/doc/74037
ER -

References

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  1. [1] K. BICHTELER, An existence theorem for strong liftings, to appear in the J. Math. Anal. and Appl. Zbl0207.12902
  2. [2] K. BICHTELER, On the strong lifting property, in manuscript. Zbl0236.46055
  3. [3] N. BOURBAKI, Intégration, Chap. I-IV (1965), and Chap. v (1967), Hermann, Paris. 
  4. [4] J. DIEUDONNÉ, Sur le théorème de Lebesgue-Nikodym, IV, J. Indian Math. Soc., N.S., 15, 77-86 (1951). Zbl0043.33001MR13,447j
  5. [5] A. IONESCU TULCEA and C. IONESCU TULCEA, On the lifting property, (IV). Disintegration of measures, Ann. Inst. Fourier, 14, 445-472 (1964). Zbl0128.34802
  6. [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). Zbl0201.49202MR35 #2997
  7. [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. Zbl0179.46303MR43 #2185
  8. [8] R. MAHER, A note on strong liftings, J. Math. Anal. and Appl., 29, 633-639 (1970). Zbl0214.07105MR43 #7584

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