Preorderings compatible with probability measures
Authors:
Rolando Chuaqui and Jerome Malitz
Journal:
Trans. Amer. Math. Soc. 279 (1983), 811-824
MSC:
Primary 60A10; Secondary 03H05
DOI:
https://doi.org/10.1090/S0002-9947-1983-0709585-3
MathSciNet review:
709585
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Abstract | References | Similar Articles | Additional Information
Abstract: The main theorem proved in this paper is:
Let be a
-complete Boolean algebra and
binary relation with field
such that:
(i) Every finite subalgebra admits a probability measure
such that for
.
(ii) If for every and
, then
.
Under these conditions there is a -additive probability measure
on
such that:
(a) If there is , such that for every
there is a
with
, and
, then we have that for every
.
(b) If for every , there is
such that
implies
, then we have that for every
implies
.
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- [V]
C. Villegas, On qualitative probability
-algebras, Ann. Math. Statist. 35 (1964), 1787-1796. MR 0167588 (29:4860)
- [SC]
M. G. Schwarze and R. Chuaqui,
-additive measurement structures, Mathematical Logic in Latin America (Arruda, Chuaqui and da Costa, eds.), North-Holland, Amsterdam, 1980, pp. 351-364. MR 573956 (81g:90009)
- [KPS] C. H. Kraft, J. W. Pratt and A. Seidenberg, Intuitive probability on finite sets, Ann. Math. Statist. 30 (1959), 408-419. MR 0102850 (21:1636)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1983-0709585-3
Article copyright:
© Copyright 1983
American Mathematical Society