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Two lifting theorems


Author: Stuart P. Lloyd
Journal: Proc. Amer. Math. Soc. 42 (1974), 128-134
MSC: Primary 46G15
DOI: https://doi.org/10.1090/S0002-9939-1974-0328588-4
MathSciNet review: 0328588
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Abstract: It is assumed that the measure algebra involved has cardinality $ {2^{{\aleph _0}}}$, and it is assumed further that $ {2^{{\aleph _0}}} = {\aleph _1}$. Then liftings exist when the $ \sigma $-field is not necessarily complete, and strong Borel liftings exist in the locally compact $ \sigma $-compact metric case.


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  • [1] A. Ionescu Tulcea and C. Ionescu Tulcea, Topics in the theory of lifting, Ergebnisse der Math. und ihrer Grenzgebiete, Band 48, Springer-Verlag, New York, 1969. MR 43 #2185. MR 0276438 (43:2185)
  • [2] S. P. Lloyd, On finitely additive set functions, Proc. Amer. Math. Soc. 14 (1963), 701-704. MR 28 #4071. MR 0160861 (28:4071)
  • [3] Zbigniew Semadeni, Banach spaces of continuous functions. I, PWN, Warsaw, 1971.
  • [4] J. von Neumann and M. H. Stone, The determination of representative elements in the residual classes of a Boolean algebra, Fund. Math. 25 (1935), 353-378.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0328588-4
Keywords: Lifting theory
Article copyright: © Copyright 1974 American Mathematical Society

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