Category:Countably Additive Functions

From ProofWiki
Jump to navigation Jump to search

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.