# 复测度　`def.complex-measure`
复测度（Complex Measure）
layer 16 · 定义 · 符号测度与分解 · 分析学
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可测空间 $(X, \mathcal{M})$ 上的**复测度**是一个映射

$$\nu : \mathcal{M} \to \mathbb{C}$$

满足

$$\nu(\emptyset) = 0, $$

且对两两不交的 $\{E_j\} \subseteq \mathcal{M}$：
> 陈述续见 [nodes/def.complex-measure.2.md](./def.complex-measure.2.md)


## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/def.complex-measure.4.md](./def.complex-measure.4.md)

## 它能推出什么 / 谁在用它
- …另有出边，续页见 [nodes/def.complex-measure.5.md](./def.complex-measure.5.md)

## English abstract · **draft** · machine-drafted, pending author review; Chinese is authoritative
> English abstract 续见 [nodes/def.complex-measure.3.md](./def.complex-measure.3.md)

refs: Folland, Real Analysis, §3.3

外部：Wikipedia https://en.wikipedia.org/wiki/Complex_measure

> 说明见 `notes/def.complex-measure.md`

引用：`def.complex-measure`（内容 v0.9.0）· 条款见 [LICENSE.txt](../LICENSE.txt)