# 乘积测度　`def.product-measure`
乘积测度（Product Measure $\mu \times \nu$）
layer 17 · 定义 · 乘积测度与 Fubini · 分析学
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设 $(X, \mathcal{M}, \mu )$ 与 $(Y, \mathcal{N}, \nu )$ 是测度空间。
> 陈述续见 [nodes/def.product-measure.2.md](./def.product-measure.2.md)


## 它能推出什么 / 谁在用它
- ⇒ [`prop.product-incomplete`](../nodes/prop.product-incomplete.md) 乘积测度通常不完备

- …另有出边，续页见 [nodes/def.product-measure.7.md](./def.product-measure.7.md)

## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/def.product-measure.5.md](./def.product-measure.5.md)

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

refs: Folland, Real Analysis, §2.5；Halmos, Measure Theory, §35

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

> 说明见 `notes/def.product-measure.md`

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