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Title

On strong liftings for projective limits

Authors 1,

Affiliations

  1. Department of Statistics, University of Piraeus, 80 Karaoli & Dimitriou St., 185 34 Piraeus, Greece

Abstract

We discuss the permanence of strong liftings under the formation of projective limits. The results are based on an appropriate consistency condition of the liftings with the projective system called "self-consistency", which is fulfilled in many situations. In addition, we study the relationship of self-consistency and completion regularity as well as projective limits of lifting topologies.

Bibliography

  1. A. G. A. G. Babiker, G. Heller and W. Strauss, On strong lifting compactness, with applications to topological vector spaces, J. Austral. Math. Soc. Ser. A 41 (1986), 211-223.
  2. A. G. A. G. Babiker and W. Strauss, Almost strong liftings and τ-additivity, in: Measure Theory, Proc. Oberwolfach, 1979, D. Kölzow (ed.), Lecture Notes in Math. 794, Springer, 1980, 220-227.
  3. A. Bellow, Lifting compact spaces, ibid., 233-253.
  4. S. Bochner, Harmonic Analysis and the Theory of Probability, Univ. of California Press, Berkeley, 1955.
  5. J. R. Choksi, Inverse limits of measure spaces, Proc. London Math. Soc. (3) 8 (1958), 321-342.
  6. J. R. Choksi, Recent developments arising out of Kakutani's work on completion regularity of measures, in: Contemp. Math. 26, Amer. Math. Soc., 1984, 8-93.
  7. J. Dixmier, Sur certains espaces considérés par M. H. Stone, Summa Brasil. Math. 2 (1951), 151-182.
  8. J. Dugundji, Topology, Allyn and Bacon, Boston, 1970.
  9. D. H. Fremlin, Products of Radon measures: A counter-example, Canad. Math. Bull. 19 (1976), 285-289.
  10. D. H. Fremlin, Losert's example, Note of 18/9/79, University of Essex, Mathematics Department.
  11. S. Graf, Schnitte Boolescher Korrespondenzen und Ihre Dualisierungen, Dissertation, Erlangen, 1973.
  12. S. Graf, On the existence of strong liftings in second countable topological spaces, Pacific J. Math. 58 (1975), 419-426.
  13. P. R. Halmos, Measure Theory, Van Nostrand Reinhold, New York, 1950.
  14. A. and C. Ionescu Tulcea, Topics in the Theory of Lifting, Springer, Berlin, 1969.
  15. K. Jacobs, Measure and Integral, Academic Press, New York, 1978.
  16. S. Kakutani, Notes on infinite product measures, II, Proc. Imperial Acad. Tokyo 19 (1943), 184-188.
  17. J. D. Knowles, Measures on topological spaces, Proc. London Math. Soc. 17 (1967), 139-156.
  18. V. Losert, A measure space without the strong lifting property, Math. Ann. 239 (1979), 119-128.
  19. N. D. Macheras, On inductive limits of measure spaces and projective limits of Lp-spaces, Mathematika 36 (1989), 116-130.
  20. N. D. Macheras, On limit permanence of projectivity and injectivity, Bull. Greek Math. Soc., to appear.
  21. N. D. Macheras and W. Strauss, On various strong lifting properties for topological measure spaces, Rend. Circ. Mat. Palermo (2) Suppl. 28 (1992), 149-162.
  22. N. D. Macheras and W. Strauss, On products of almost strong liftings, J. Austral. Math. Soc., to appear.
  23. D. Maharam, On a theorem of von Neumann, Proc. Amer. Math. Soc. 9 (1958), 987-994.
  24. W. Moran, The additivity of measures on completely regular spaces, J. London Math. Soc. 43 (1968), 633-639.
  25. K. Musiał, Projective limits of perfect measure spaces, Fund. Math. 110 (1980), 163-189.
  26. J. von Neumann, Algebraische Repräsentanten der Funktionen bis auf eine Menge von Masse Null, J. Reine Angew. Math. 165 (1931), 109-115.
  27. S. Okada and Y. Okazaki, Projective limit of infinite Radon measures, J. Austral. Math. Soc. Ser. A 25 (1978), 328-331.
  28. J. C. Oxtoby, Measure and Category, Springer, Berlin, 1970.
  29. M. M. Rao, Projective limits of probability spaces, J. Multivariate Anal. 1 (1971), 28-57 .
  30. M. Talagrand, Closed convex hull of set of measurable functions, Riemann-measurable functions and measurability of translations, Ann. Inst. Fourier (Grenoble) 32 (1) (1982), 39-69.
  31. T. Traynor, An elementary proof of the lifting theorem, Pacific J. Math. 53 (1974), 267-272.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm144/fm14432.pdf

Fundamenta Mathematicae
1994/144/3
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Pages:
209-229
Main language of publication
English
Received
1992-10-12
Accepted
1993-07-20
Published
1994
Exact and natural sciences