# Category:Definitions/Total Variation (Measure Theory)

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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.