# Probability space

## Sample space, event, outcome

Definition: Sample space
A sample space S is just a set. We refer to the elements of S as outcomes. We refer to the subsets of S as events.

## Probability measure, Kolmogorov's axioms

A probability measure on a sample space S is a function satisfying the following three properties:
1. For all events ,
2. For all disjoint events and ,
These three properties are referred to as the Kolmogorov axioms.

## Probability space

Definition: Probability space
A probability space is just a pair containing a sample space S and a probability measure on S.