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

## Probability space

**Sample space** $\Omega$ is a set of elementary events.
A sigma-algebra $\Sigma$ of a sample space consists of
all the events that can be measured using some instrument.

**Probability measure** $P$ of a measurable sample space $(\Omega, \Sigma)$
is a normalized finite measure: $P(\Omega) = 1$.
Any finite measure can be normalized into a probablity measure.

**Probability space** $(\Omega, \Sigma, P)$
is a sample space $\Omega$ assigned with a probability measure $P$ on its measureable sets $\Sigma$.

## Conditional probability

## Total probability equation, Bayes formular

## Independence

🏷 Category=Probability