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Definitions Axioms Theorems

Definitions establish the logic of probability theory

axioms are facts that we accept without proof

Theorems are consequences that follow logically from definitions and axioms

Example.

Definition (정의)

A probability measure P[*] is a function that maps events in the sample space to real numbers 

Axiom (공리)

Axiom 1.  For any event A, P[A] >= 0
Axiom 2.  P[S] = 1
Axiom 3.  For any countable collection A1, A2, ... of mutually exclusive events

Theorem (정리)

De Morgan's law relates all three basic operations :

Reference
- Probability and stochastic processes by Yates and Goodman