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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.
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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
(52 #8372)
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J.
L. Bell and A.
B. Slomson, Models and ultraproducts: An introduction,
North-Holland Publishing Co., Amsterdam, 1969. MR 0269486
(42 #4381)
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Chen-chung
Chang and H.
Jerome Keisler, Continuous model theory, Annals of Mathematics
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(38 #36)
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Kai
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(49 #11579)
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Alan
McK. Shorb, Completely additive measure and
integration, Proc. Amer. Math. Soc.
53 (1975), no. 2,
453–459. MR 0382578
(52 #3461), http://dx.doi.org/10.1090/S0002-9939-1975-0382578-5
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T. Q. Sibley, The theory of finitely additive probability using non-standard analysis, Ph.D. dissertation, Boston University, 1980.
- [1]
- W. D. L. Appling, A Fubini-type theorem for finitely additive measure spaces, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 1 (1974), 155-166. MR 0387532 (52:8372)
- [2]
- J. L. Bell and A. B. Slomson, Models and ultraproducts: An introduction, North-Holland, Amsterdam, 1969. MR 0269486 (42:4381)
- [3]
- C. C. Chang and H. J. Keisler, Continuous model theory, Princeton Univ. Press, Princeton, N.J., 1966. MR 0231708 (38:36)
- [4]
- K. L. Chung, A course in probability theory, Academic Press, New York, 1974. MR 0346858 (49:11579)
- [5]
- A. McK. Shorb, Completely additive measure and integration, Proc. Amer. Math. Soc. 53 (1975), 453-459. MR 0382578 (52:3461)
- [6]
- T. Q. Sibley, The theory of finitely additive probability using non-standard analysis, Ph.D. dissertation, Boston University, 1980.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1982-0643749-7
PII:
S 0002-9939(1982)0643749-7
Keywords:
Finitely additive probability,
ultrafilter limits,
infinitely divisible laws,
characteristic functions,
ultrafilters,
nonstandard analysis
Article copyright:
© Copyright 1982 American Mathematical Society
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