Two lifting theorems
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- by Stuart P. Lloyd PDF
- Proc. Amer. Math. Soc. 42 (1974), 128-134 Request permission
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.References
- A. Ionescu Tulcea and C. Ionescu Tulcea, Topics in the theory of lifting, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 48, Springer-Verlag New York, Inc., New York, 1969. MR 0276438
- S. P. Lloyd, On finitely additive set functions, Proc. Amer. Math. Soc. 14 (1963), 701–704. MR 160861, DOI 10.1090/S0002-9939-1963-0160861-8 Zbigniew Semadeni, Banach spaces of continuous functions. I, PWN, Warsaw, 1971. 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.
Additional Information
- © Copyright 1974 American Mathematical Society
- 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