Scaled Boolean Algebras

Details Scaled Boolean Algebras Scaled Boolean Algebras

2002-03-23

arxiv.org/abs/math/0203249v1

Mathematics

Probability

53 pages, 8 Postscript figures, Uses ajour.sty from Academic Press, To appear in Advances in Applied Mathematics

Scientific paper

Scaled Boolean algebras are a category of mathematical objects that arose from attempts to understand why the conventional rules of probability should hold when probabilities are construed, not as frequencies or proportions or the like, but rather as degrees of belief in uncertain propositions. This paper separates the study of these objects from that not-entirely-mathematical problem that motivated them. That motivating problem is explicated in the first section, and the application of scaled Boolean algebras to it is explained in the last section. The intermediate sections deal only with the mathematics. It is hoped that this isolation of the mathematics from the motivating problem makes the mathematics clearer.

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