Definition:Variation/Signed Measure

Definition
Let $\struct {X, \Sigma}$ be a measurable space.

Let $\mu$ be a signed measure on $\struct {X, \Sigma}$.

Let $\struct {\mu^+, \mu^-}$ be the Jordan decomposition of $\mu$.

We define the variation $\size \mu$ of $\mu$ by:


 * $\size \mu = \mu^+ + \mu^-$

Also see

 * Variation of Signed Measure is Measure