Ultrafilter limits and finitely additive probability
HTML articles powered by AMS MathViewer
- by Thomas Q. Sibley PDF
- Proc. Amer. Math. Soc. 84 (1982), 560-562 Request permission
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.References
- 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 387532
- J. L. Bell and A. B. Slomson, Models and ultraproducts: An introduction, North-Holland Publishing Co., Amsterdam-London, 1969. MR 0269486
- Chen-chung Chang and H. Jerome Keisler, Continuous model theory, Annals of Mathematics Studies, No. 58, Princeton University Press, Princeton, N.J., 1966. MR 0231708
- Kai Lai Chung, A course in probability theory, 2nd ed., Probability and Mathematical Statistics, Vol. 21, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1974. MR 0346858
- Alan McK. Shorb, Completely additive measure and integration, Proc. Amer. Math. Soc. 53 (1975), no. 2, 453–459. MR 382578, DOI 10.1090/S0002-9939-1975-0382578-5 T. Q. Sibley, The theory of finitely additive probability using non-standard analysis, Ph.D. dissertation, Boston University, 1980.
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 560-562
- MSC: Primary 60E10; Secondary 28A60, 60E07
- DOI: https://doi.org/10.1090/S0002-9939-1982-0643749-7
- MathSciNet review: 643749