查看“︁火腿三明治定理”︁的源代码

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[[File:Théorème-du-sandwich.jpg|thumb|火腿三明治定理的图解。]]
'''火腿三明治定理'''（'''{{lang-en|Ham sandwich theorem}}'''），也被称为Stone-Tukey定理，它在[[测度论]]中有重要的意义。火腿三明治定理说明在n-维[[向量空間|空间]]中有n个可[[测度|测量]]的“物体”，可以用一个(n-1)-维的[[超平面]]把它们同時分成[[測度]]相等的两部分。

== 命名 ==
当 n=3 时，就像一个三明治一样——这里的三个“物体”则是两片面包和中间的火腿。用一个平面可以同时把三个“物体”截断。

== 二維版本的證明：「旋轉刀片」 ==
二維版本的證明比任意維度的證明較為簡單，流程如下：

對任何角度<math>\alpha\in[0,\pi]</math>，均存在一條與 X 軸成角度<math>\alpha</math>的直線平分第一個物體。（需使用[[介值定理]]）
令<math>\alpha</math>由 0 增加到 <math>\pi</math>，再使用介值定理，則存在一條直線同時平分第二個物體。

== 定理的離散版本 ==
離散版本可以視為定理的特例，當中每一個＂物體＂都是用有限個點組成的集合，並使用[[計數測度]]。但需要考慮點剛好落左超平面上時的情況。

[[Category:拓扑学]]
[[Category:拓撲學理論]]

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