Definition:Variation/Signed Measure/Definition 1

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:

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

Sources

• 2013: Donald L. Cohn: Measure Theory (2nd ed.) ... (previous) ... (next): $4.1$: Signed and Complex Measures