Probability distribution

A probability distribution is defined by the tupel $(\mathrm{\Omega },𝒮,P)$ where

• $\mathrm{\Omega }$ is the set of all possible results of an random experiment,
• $𝒮$ is $\sigma$-algebra as special subset of power set of $\mathrm{\Omega }$, to which a probility can be assigned.
• $P:𝒮\to [0,1]$ is the probability measure on the $\sigma$-algebra.

σ-Algebra

The concept of the sigma-algebra had to introduced in the probability theory, because there exists a /measurment problem/.