Re: Axioms for elementary probability

On Thursday 07 May 2009 08:14:01 David Espinosa wrote:

Here's a question about elementary (naive, finitist) probability. The proper, self-dual axioms for elementary probability are presumably

P(0) = 0 P(X) = 1 P(A u B) + P(A n B) = P(A) + P(B)

P's domain is a boolean algebra. P's codomain is [0,1]. I'm wondering, what kind of algebraic structure is [0,1] in this case?

It is a partial algebra with partial operations \wedge, v, +, o, 0, 1 (the order can be written with \wedge, v) a+b is defined iff a+b =< 1 in R a o b is always defined (multiplication) plenty of strong weak equalities hold. What is the generalization to categories? Best A. Mani -- A. Mani CLC, ASL, AMS, CMS http://amani.topcities.com