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

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