# Probability Axioms

Traditional probability is based on Kolmogorov's three axioms of probability. Because they are axioms they don't require a proof and although they are intuitive I am wondering if there is a more rigorous way to be convinced of their validity other than intuition.

• You could treat them as a definition of a probability measure, in contrast to other measures which might not necessarily sum to $1$ or always be non-negative, or without countable disjoint additivity. – Henry Jan 13 '17 at 19:56
• The book by Dubins & Savage: How to gamble if you must. explores a probability system in which $P(A \cup B) = P(A) + P(B)$ for disjoint $A,B,$ but in which countable additivity is not included among the axioms. – BruceET Jan 13 '17 at 23:46