Interpretations of Probability (Stanford Encyclopedia of Philosophy)
CRANK

1. Kolmogorov's Probability CalculusProbability theory was a relative latecomer in intellectual history. It was inspired by games of chance in 17th century France and inaugurated by the Fermat-Pascal correspondence. However, its axiomatization had to wait until Kolmogorov's classic Foundations of the Theory of Probability (1933). Let Ω be a non-empty set (‘the universal set’). A field (or algebra) on Ω is a set F of subsets of Ω that has Ω as a member, and that is closed under complementation (with respect to Ω) and union. Let P be a function from F to the real numbers obeying:(Non-negativity) P(A) ≥ 0, for all A ∈ F.(Normalization) P(Ω) = 1.(Finite additivity) P(A ∪ B) = P(A) + P(B) for all A, B ∈ F such that A ∩ B = ∅.Call P a probability function, and (Ω, F, P) a probability space.The assumption that P is defined on a field guarantees that these axioms are non-vacuously instantiated, as are the various theorems that follow from them. The non-negativity and normalizat…

plato.stanford.edu
Related Topics: Objective C