# 截口　`def.section`
English entry · root `../`
[in graph](../#n=def.section)　·　[Chinese page (authoritative)](./def.section.md)

> English: **draft** · machine-drafted, pending author review; the Chinese page is authoritative.

layer 6 · definition · cluster 乘积测度与 Fubini (`analysis.product`) · Analysis

## Abstract
For $E \subseteq X \times Y$ the vertical and horizontal sections are $E_x := \{y \in Y : (x,y) \in E\}$ and $E^y := \{x \in X : (x,y) \in E\}$; for a function $f : X \times Y \to \mathbb{C}$ one sets $f_x(y) = f^y(x) = f(x,y)$. Geometrically, cut the picture with a line and look at what remains. Sections are the language in which Fubini is stated: integrate along the sections first, then integrate the resulting function against the other variable.

> 续见 nodes/def.section.en.2.md