Probability distribution

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

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

The concept of the sigma-algebra had to introduced in the probability theory, because there exists a measurment problem^[1].

1. ↑ measurement problem - see Germany Wikipedia Article w:de:Maßproblem „Maßproblem“. In: German Wikipedia, The Free Encyclopedia, 2017 August 26, 15:33 UTC. URL: https://de.wikipedia.orghttps://en.wikiversity.org/w/index.php?title=Ma%C3%9Fproblem&oldid=168500347 (accessed: 2017/12/31, 08:22 UTC)