Category:Countably Additive Functions
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This category contains results about Countably Additive Functions.
Let $\Sigma$ be a $\sigma$-algebra.
Let $f: \Sigma \to \overline \R$ be a function, where $\overline \R$ denotes the set of extended real numbers.
Then $f$ is defined as countably additive if and only if:
- $\ds \map f {\bigcup_{n \mathop \in \N} E_n} = \sum_{n \mathop \in \N} \map f {E_n}$
where $\sequence {E_n}$ is any sequence of pairwise disjoint elements of $\Sigma$.
Pages in category "Countably Additive Functions"
The following 2 pages are in this category, out of 2 total.