# 积空间与实虚部　`prop.measurable-product-and-realimag`
命题：可测函数到积空间；f 可测 $\iff$ 实部虚部可测
layer 7 · 命题 · 可测函数与收敛 · 分析学
[在星图里打开](../#n=prop.measurable-product-and-realimag)　·　[节点索引](../index.md)

**(1)** 设 $(X, \mathcal{M})$、$(Y_\alpha , \mathcal{N}_\alpha ) (\alpha \in A)$ 是可测空间，$Y = \prod_{\alpha} Y_\alpha$，$\mathcal{N} = \otimes _{\alpha} \mathcal{N}_\alpha$，$\pi _\alpha : Y \to Y_\alpha$ 是投影。则
> 陈述续见 [nodes/prop.measurable-product-and-realimag.2.md](./prop.measurable-product-and-realimag.2.md)


## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/prop.measurable-product-and-realimag.3.md](./prop.measurable-product-and-realimag.3.md)

refs: Folland, Real Analysis, Prop. 2.3

> 说明见 `notes/prop.measurable-product-and-realimag.md`

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