Extensions of measures and the von Neumann selection theorem
Author:
Arthur Lubin
Journal:
Proc. Amer. Math. Soc. 43 (1974), 118-122
MSC:
Primary 28A10
DOI:
https://doi.org/10.1090/S0002-9939-1974-0330393-X
MathSciNet review:
0330393
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Let be a Blackwell space, where
is the
-algebra of Borel sets. Then if
is a finite measure defined on a countably generated sub-
-algebra
can be extended to a Borel measure
. Equivalently, if
and
are Blackwell and
is Borel, and
is a Borel measure carried on
, then there exists a Borel measure
on
with
, where
. We characterize
if
is semischlicht.
- [1] Paul R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, N. Y., 1950. MR 0033869
- [2] Felix Hausdorff, Set theory, Second edition. Translated from the German by John R. Aumann et al, Chelsea Publishing Co., New York, 1962. MR 0141601
- [3] K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. MR 0217751
- [4] N. Lusin, Leçons sur les ensembles analytiques, Hermann, Paris, 1930.
- [5] Paul-A. Meyer, Probability and potentials, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. MR 0205288
- [6] John von Neumann, On rings of operators. Reduction theory, Ann. of Math. (2) 50 (1949), 401–485. MR 29101, https://doi.org/10.2307/1969463
- [7] H. L. Royden, Real analysis, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. MR 0151555
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A10
Retrieve articles in all journals with MSC: 28A10
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1974-0330393-X
Article copyright:
© Copyright 1974
American Mathematical Society