Ultrafilter limits and finitely additive probability

Author:
Thomas Q. Sibley

Journal:
Proc. Amer. Math. Soc. **84** (1982), 560-562

MSC:
Primary 60E10; Secondary 28A60, 60E07

MathSciNet review:
643749

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Abstract: Ultrafilter limits provide the natural convergence notion for finitely additive probability. The finitely additive infinitely divisible laws are closed under ultrafilter limits. The characteristic function of any convolution of finitely additive probability measures is the product of their characteristic functions.

**[1]**William D. L. Appling,*A Fubini-type theorem for finitely additive measure spaces*, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)**1**(1974), 155–166 (1975). MR**0387532****[2]**J. L. Bell and A. B. Slomson,*Models and ultraproducts: An introduction*, North-Holland Publishing Co., Amsterdam-London, 1969. MR**0269486****[3]**Chen-chung Chang and H. Jerome Keisler,*Continuous model theory*, Annals of Mathematics Studies, No. 58, Princeton Univ. Press, Princeton, N.J., 1966. MR**0231708****[4]**Kai Lai Chung,*A course in probability theory*, 2nd ed., Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Probability and Mathematical Statistics, Vol. 21. MR**0346858****[5]**Alan McK. Shorb,*Completely additive measure and integration*, Proc. Amer. Math. Soc.**53**(1975), no. 2, 453–459. MR**0382578**, 10.1090/S0002-9939-1975-0382578-5**[6]**T. Q. Sibley,*The theory of finitely additive probability using non-standard analysis*, Ph.D. dissertation, Boston University, 1980.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1982-0643749-7

Keywords:
Finitely additive probability,
ultrafilter limits,
infinitely divisible laws,
characteristic functions,
ultrafilters,
nonstandard analysis

Article copyright:
© Copyright 1982
American Mathematical Society