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Rado's theorem for the Loeb space of an internal $ *$-finitely additive measure space


Author: Boško Živaljević
Journal: Proc. Amer. Math. Soc. 112 (1991), 203-207
MSC: Primary 03H05; Secondary 28A05
DOI: https://doi.org/10.1090/S0002-9939-1991-1056688-2
MathSciNet review: 1056688
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Abstract: A version of Rado's theorem about the existence of a family of subsets of a given family of sets combinatorially similar to another family of sets is proved for the Loeb space of an internal $ *$-finitely additive measure space. As a corollary we obtain the Loeb measured case of the result of B. Bollobas and N. Th. Varopoulos about the existence of a family of mutually disjoint measurable subsets of the given family of measurable sets, having the prescribed measure.


References [Enhancements On Off] (What's this?)

  • [BoV] B. Bollobas and N. Th. Varopoulos, Representation of systems of measurable sets, Math. Proc. Cambridge Philos. Soc. 78 (1974), 323-325. MR 0379781 (52:686)
  • [Ha] P. Hall, On representatives of subsets, J. London Math. Soc. 10 (1935), 26-30.
  • [HuLo] A. E. Hurd and P. A. Loeb, An introduction to nonstandard real analysis, Academic Press, New York, 1985. MR 806135 (87d:03184)
  • [LaRo] D. Landers and L. Rogge, Universal Loeb-measurability of sets and of the standard part map with applications, Trans. Amer. Math. Soc. 304 (1983), 229-243. MR 906814 (89d:28015)
  • [Lo] P. A. Loeb, Conversion from nonstandard to standard measure space and applications in probability theory, Trans. Amer. Math. Soc. 211 (1975), 113-122. MR 0390154 (52:10980)
  • [Ra] R. Rado, A theorem on general measure function, Proc. London Math. Soc. 44 (1938), 61-91.
  • [StBa] K. D. Stroyan and J. M. Bayod, Foundations of infinitesimal stochastic analysis, North-Holland, Amsterdam, 1986. MR 849100 (87m:60001)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1056688-2
Article copyright: © Copyright 1991 American Mathematical Society

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