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

Živaljević, Boško

doi:10.1090/S0002-9939-1991-1056688-2

Rado’s theorem for the Loeb space of an internal $*$-finitely additive measure space
HTML articles powered by AMS MathViewer

by Boško Živaljević

Proc. Amer. Math. Soc. 112 (1991), 203-207

DOI: https://doi.org/10.1090/S0002-9939-1991-1056688-2

PDF | Request permission

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

B. Bollobás and N. Th. Varopoulos, Representation of systems of measurable sets, Math. Proc. Cambridge Philos. Soc. 78 (1975), no. 2, 323–325. MR 379781, DOI 10.1017/S0305004100051756

On representatives of subsets

10

Albert E. Hurd and Peter A. Loeb, An introduction to nonstandard real analysis, Pure and Applied Mathematics, vol. 118, Academic Press, Inc., Orlando, FL, 1985. MR 806135
D. Landers and L. Rogge, Universal Loeb-measurability of sets and of the standard part map with applications, Trans. Amer. Math. Soc. 304 (1987), no. 1, 229–243. MR 906814, DOI 10.1090/S0002-9947-1987-0906814-1
Peter A. Loeb, Conversion from nonstandard to standard measure spaces and applications in probability theory, Trans. Amer. Math. Soc. 211 (1975), 113–122. MR 390154, DOI 10.1090/S0002-9947-1975-0390154-8

A theorem on general measure function

44

K. D. Stroyan and José Manuel Bayod, Foundations of infinitesimal stochastic analysis, Studies in Logic and the Foundations of Mathematics, vol. 119, North-Holland Publishing Co., Amsterdam, 1986. MR 849100