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# Sigma algebra

A **sigma algebra** is family of subsets, ℱ say, of some set Ω such that

For the set of real numbers the most common sigma algebra is the Borel sigma algebra, denoted ℬ(ℝ). This is the smallest sigma algebra that contains all open intervals.

- Ω∈ℱ,
- If A∈ℱ then A
^{c}=Ω∖A∈ℱ, - If A
_{k}, k=1,2,...∈ℱ then ⋃_{ k}A_{k}∈ℱ.

For the set of real numbers the most common sigma algebra is the Borel sigma algebra, denoted ℬ(ℝ). This is the smallest sigma algebra that contains all open intervals.

Questions: Magnus Wiktorsson

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