Definition: SigmaAlgebra
A system of subsets \({\mathcal {A}}\) on a set \(M\) is called a \(\sigma \)algebra (read "sigmaalgebra") if the following conditions are fulfilled:
 \(M\in {\mathcal {A}}\).
 With \(T\in {\mathcal {A}}\) also the set complement \(M\setminus T\) is contained in \({\mathcal {A}}\).
 For each countable family \(T_{i}\in {\mathcal {A}}\), \(i\in I\), we have \(\bigcup _{i\in I}T_{i}\in {\mathcal {A}}.\)
Table of Contents
 Definition: Measurable Set
 Definition: Measureable Function
 Definition: Measure
 Definition: Premeasure
 Definition: Measurable Space
Mentioned in:
Definitions: 1 2 3 4 5
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References
Adapted from CC BYSA 3.0 Sources:
 Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of OsnabrÃ¼ck