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Remarks on the strong lifting property for products

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Abstract

The class of compact measure spaces which possesses the attribute of having products with the strong lifting property is much larger than that of the metric spaces. This class includes every homogeneous space equipped with a quasi-invariant measure. This result, in conjunction with Losert’s example and Kupka’s arguments, yields invariant measures on transformation groups, which fail to have a lifting commuting with left translations. In addition, the previously mentioned class contains every product measure on an arbitrary product of metrizable spaces.

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References

  1. K. Bichteler,On the strong lifting property, Illinois J. Math.16 (1972), 370–379.

    MATH  MathSciNet  Google Scholar 

  2. N. Bourbaki,Integration, Hermann, Paris, 1965.

    MATH  Google Scholar 

  3. J. R. Choksi and D. H. Fremlin,Completion regular measures on product spaces, Math. Ann.241 (1979), 113–128.

    Article  MATH  MathSciNet  Google Scholar 

  4. S. Grekas,On the strong lifting property for products, Bull. Greek Math. Soc. (to appear).

  5. A. Ionescu Tulcea and C. Ionescu Tulcea,Topics in the Theory of Lifting, Springer-Verlag, Berlin-Heidelberg-New York, 1969.

    MATH  Google Scholar 

  6. R. A. Johnson,Existence of a strong lifting commuting with a compact group of transformations II, Pac. J. Math.82 (1979), 457–461.

    MATH  Google Scholar 

  7. R. A. Johnson,Disintegrating measures on compact group extensions, Z. Wahrscheinlichkeitstheor. Verw. Geb.53 (1980), 271–281.

    Article  MATH  Google Scholar 

  8. J. Kupka,Strong liftings with application to measurable cross sections in locally compact groups, Isr. J. Math.44 (1983), 243–261.

    Article  MATH  MathSciNet  Google Scholar 

  9. V. Losert,A measure space without the strong lifting property, Math. Ann.239 (1979), 119–128.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Athens, Panepistemiopolis, 15781, Athens, Greece

    S. Grekas

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  1. S. Grekas
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Grekas, S. Remarks on the strong lifting property for products. Israel J. Math. 58, 198–204 (1987). https://doi.org/10.1007/BF02785677

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  • DOI: https://doi.org/10.1007/BF02785677

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