Probability distribution

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

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

## σ-Algebra

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

## References

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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=Maßproblem&oldid=168500347 (accessed: 2017/12/31, 08:22 UTC)