The Kolmogorov axioms are an axiomatization of probability theory.
Axioms[]
Let be function such that is a sigma-algebra on the set . Then is a probablity measure if the following holds:
- For all
- For all , if then
The ordered pair ) is called a probablity space. Here, is called the Sample space, is a collection of events, and is said to be the probablity measure.
It follows by induction on statement 3 that:
Important Consequences[]
- Complement Rule
- Addition Theorem of Probablity
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