ABSTRACT
The axiomatic foundation of modern probability theory was originally formalized in Andrey Kolmogorov’s Foundations of the Theory of Probability (Kolmogorov (1933)) based on the concept of a measure, giving formal rules for the consistent assignment of probabilities. The set of all possible outcomes is well defined, denoted , and the probability that a random outcome ω∈ is in E⊂ is assigned a number P(E) under the following three axioms:
(i) P(E)≥0, (ii) P()=1, (iii) If E1,E2, . . . is a countable collection of disjoint subsets of then P(∪iEi)=∑
i≥1 P(Ei).
