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Definition: Sigma-Algebra

A system of subsets \({\mathcal {A}}\) on a set \(M\) is called a \(\sigma \)-algebra (read "sigma-algebra") 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

1. Definition: Measurable Set
2. Definition: Measureable Function
3. Definition: Measure
4. Definition: Pre-measure
5. Definition: Measurable Space

Mentioned in:

Definitions: 1 2 3 4 5

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References

Adapted from CC BY-SA 3.0 Sources:

1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück