Category:Definitions/Total Variation (Measure Theory)
Jump to navigation
Jump to search
This category contains definitions related to Total Variation (Measure Theory) in the context of Measure Theory.
Related results can be found in Category:Total Variation (Measure Theory).
Signed Measure
Let $\struct {X, \Sigma}$ be a measurable space.
Let $\mu$ be a signed measure on $\struct {X, \Sigma}$.
Let $\size \mu$ be the variation of $\mu$.
We define the total variation $\norm \mu$ of $\mu$ by:
- $\norm \mu = \map {\size \mu} X$
Complex Measure
Let $\struct {X, \Sigma}$ be a measurable space.
Let $\mu$ be a complex measure on $\struct {X, \Sigma}$.
Let $\cmod \mu$ be the variation of $\mu$.
We define the total variation $\norm \mu$ of $\mu$ by:
- $\norm \mu = \map {\cmod \mu} X$
Pages in category "Definitions/Total Variation (Measure Theory)"
The following 3 pages are in this category, out of 3 total.