Kolmogorov Probability Theory

A Kolmogorov Probability Theory is an axiomatization theory for probability functions based on Kolmogorov Probability Function Axioms as proposed in (Kolmogorov, 1933).

• Context:
  • It can be for infinite probability spaces or for ...
  • It can have Theory Implications such as:
    • Any countable sequence of pairwise Disjoint Events E₁,E₂,... satisfies P(E₁ ∪ E₂ ∪ ...) = Sum_i P(E_i).
    • P(Ω - E) = 1 - P(E).
      • P(Ø) = 0. The Probability of no Event is 0.
    • P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
      • Events A and B are Conditionally Independent iff P(A & B) = P(A)*P(B).
  • …
• Counter-Example(s):
  • Bayes' Theorem.
• See: Measure Space.

---

---