# 相互奇异　`def.mutually-singular`
相互奇异 / 互相垂直（Mutually Singular $\mu \perp \nu$）
layer 16 · 定义 · 符号测度与分解 · 分析学
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两个测度（或符号测度）$\mu, \nu$ **相互奇异**，记作 $\mu \perp  \nu$，当且仅当存在 $E, F \in \mathcal{M}$ 使

$$E \cap F = \emptyset, \quad  E \cup F = X, $$

且 **$E$ 是 $\mu$零集、$F$ 是 $\nu$零集**。

## 为什么成立（入边，证明在 proofs/）
- [`def.null-set`](../nodes/def.null-set.md) 零集与完备：用到了定义 零集与完备　[proofs/def-dep.null-set-mutually-singular.md](../proofs/def-dep.null-set-mutually-singular.md)

- …另有入边，续页见 [nodes/def.mutually-singular.2.md](./def.mutually-singular.2.md)

## 它能推出什么 / 谁在用它
- …另有出边，续页见 [nodes/def.mutually-singular.3.md](./def.mutually-singular.3.md)

refs: Folland, Real Analysis, §3.2

> 说明见 `notes/def.mutually-singular.md`

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