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 .

**[**David H. Krantz, R. Duncan Luce, Patrick Suppes, and Amos Tversky,**KLST**]*Foundations of measurement*, Academic Press, New York-London, 1971. Vol. 1: Additive and polynomial representations. MR**0459067****[**C. Villegas,**V**]*On qualitative probability 𝜎-algebras*, Ann. Math. Statist.**35**(1964), 1787–1796. MR**0167588**, https://doi.org/10.1214/aoms/1177700400**[**M. G. Schwarze and R. Chuaqui,**SC**]*Axiomatizations for 𝜎-additive measurement structures*, Mathematical logic in Latin America (Proc. IV Latin Amer. Sympos. Math. Logic, Santiago, 1978) Stud. Logic Foundations Math., vol. 99, North-Holland, Amsterdam-New York, 1980, pp. 351–364. MR**573956****[**Charles H. Kraft, John W. Pratt, and A. Seidenberg,**KPS**]*Intuitive probability on finite sets*, Ann. Math. Statist.**30**(1959), 408–419. MR**0102850**, https://doi.org/10.1214/aoms/1177706260

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DOI:
https://doi.org/10.1090/S0002-9947-1983-0709585-3

Article copyright:
© Copyright 1983
American Mathematical Society