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 $P(\Omega)=1$.

## Conditional probability

## Total probability equation, Bayes formular

## Independence

🏷 Category=Probability