Kolmogorov [@Kolmogorov1956] laid the foundation of axiomatic probability theory.

## Probability space

A probability space is a measurable (sample) space assigned with a probability measure. Symbolically, it's a triplet $(\Omega, \Sigma, P)$.

Sample space $\Omega$ is the collection of elementary events.

The sigma-algebra $\Sigma$ of the sample space is all the entities that can be measured using some instrument.

A probability measure $P$ of the sample space is a normalized finite measure. That is, a measure over the sigma-algebra $\Sigma$ and $P(\Omega)=1$.