Category:Variation of Complex Measure
Jump to navigation
Jump to search
This category contains results about Variation of Complex Measure.
Definitions specific to this category can be found in Definitions/Variation of Complex Measure.
Let $\struct {X, \Sigma}$ be a measurable space.
Let $\mu$ be a complex measure on $\struct {X, \Sigma}$.
Let $\map P A$ be the set of finite partitions of $A$ into $\Sigma$-measurable sets.
We define the variation $\cmod \mu : \Sigma \to \R$ of $\mu$ by:
- $\ds \map {\cmod \mu} A = \sup \set {\sum_{j \mathop = 1}^n \cmod {\map \mu {A_j} } : \set {A_1, A_2, \ldots, A_n} \in \map P A}$
for each $A \in \Sigma$, where the supremum is taken in the set of extended real numbers $\overline \R$.
Subcategories
This category has only the following subcategory.
Pages in category "Variation of Complex Measure"
This category contains only the following page.