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
MathSciNet review: 709585
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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