On the nonstandard representation of measures
Author:
C. Ward Henson
Journal:
Trans. Amer. Math. Soc. 172 (1972), 437446
MSC:
Primary 28A25; Secondary 02H25
MathSciNet review:
0315082
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Abstract: In this paper it is shown that every finitely additive probability measure on which assigns 0 to finite sets can be given a nonstandard representation using the counting measure for some finite subset of . Moreover, if is countably additive, then can be chosen so that for every integrable function . An application is given of such representations. Also, a simple nonstandard method for constructing invariant measures is presented.
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 S. Banach, Sur le problème a la mesure, Fund. Math. 4 (1923), 733.
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 A. R. Bernstein and F. Wattenberg, Nonstandard measure theory, Internat. Sympos. Applications of Model Theory to Algebra, Analysis, and Probability (Pasadena, Calif., 1967), Holt, Rinehart and Winston, New York, 1969, pp. 171185. MR 40 #287. MR 0247018 (40:287)
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 A. Robinson, On generalized limits and linear functionals, Pacific J. Math. 14 (1964), 269283. MR 29 #1534. MR 0164235 (29:1534)
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 , Nonstandard analysis, NorthHolland, Amsterdam, 1966. MR 34 #5680. MR 0205854 (34:5680)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197203150822
PII:
S 00029947(1972)03150822
Article copyright:
© Copyright 1972
American Mathematical Society
