# 截口可测　`prop.section-measurable`
命题：可测集的截口可测，可测函数的截口可测
layer 7 · 命题 · 乘积测度与 Fubini · 分析学
[在星图里打开](../#n=prop.section-measurable)　·　[节点索引](../index.md)

**(a)** 若 $E \in \mathcal{M} \otimes  \mathcal{N}$，则对一切 $x \in X$ 有 $E_x \in \mathcal{N}$，对一切 $y \in Y$ 有 $E^y \in \mathcal{M}$。
> 陈述续见 [nodes/prop.section-measurable.2.md](./prop.section-measurable.2.md)


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

## 它能推出什么 / 谁在用它
- …另有出边，续页见 [nodes/prop.section-measurable.7.md](./prop.section-measurable.7.md)

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

refs: Folland, Real Analysis, Prop. 2.34

> 说明见 `notes/prop.section-measurable.md`

引用：`prop.section-measurable`（内容 v0.9.0）· 条款见 [LICENSE.txt](../LICENSE.txt)