On the nonstandard representation of measures
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- by C. Ward Henson PDF
- Trans. Amer. Math. Soc. 172 (1972), 437-446 Request permission
Abstract:
In this paper it is shown that every finitely additive probability measure $\mu$ on $S$ which assigns 0 to finite sets can be given a nonstandard representation using the counting measure for some $^ \ast$-finite subset $F$ of $^ \ast S$. Moreover, if $\mu$ is countably additive, then $F$ can be chosen so that \[ \int {fd\mu } = {\text {st( }}\frac {1}{{||F||}}\sum _{p \in F} ^\ast f(p))\] for every $\mu$-integrable function $f$. An application is given of such representations. Also, a simple nonstandard method for constructing invariant measures is presented.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 172 (1972), 437-446
- MSC: Primary 28A25; Secondary 02H25
- DOI: https://doi.org/10.1090/S0002-9947-1972-0315082-2
- MathSciNet review: 0315082