# Category:Complex Measures

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This category contains results about **Complex Measures**.

Definitions specific to this category can be found in **Definitions/Complex Measures**.

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

Let $\mu : \Sigma \to \C$ be a function.

We say that $\mu$ is a **complex measure** on $\struct {X, \Sigma}$ if and only if:

\((1)\) | $:$ | \(\ds \map \mu \O \) | \(\ds = \) | \(\ds 0 \) | |||||

\((2)\) | $:$ | \(\ds \forall \sequence {S_n}_{n \mathop \in \N} \subseteq \Sigma: \forall i, j \in \N: S_i \cap S_j = \O:\) | \(\ds \map \mu {\bigcup_{n \mathop = 1}^\infty S_n} \) | \(\ds = \) | \(\ds \sum_{n \mathop = 1}^\infty \map \mu {S_n} \) | that is, $\mu$ is a countably additive function |

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "Complex Measures"

The following 10 pages are in this category, out of 10 total.