Loomis and Whitney proved an inequality between volume and areas of projections of an open set in n-dimensional space related to the isoperimetric inequality. They reduced the problem to a combinatorial theorem proved by a repeated use of Hölder inequality. In this paper we prove a general inequality between real numbers which easily implies the combinatorial theorem of Loomis and Whitney.

中文翻译：

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卢米斯-惠特尼定理的基本证明

Loomis 和 Whitney 证明了与等周不等式相关的n维空间中开集的体积和投影面积之间的不等式。他们将问题简化为通过重复使用 Hölder 不等式证明的组合定理。在本文中，我们证明了实数之间的一般不等式，这很容易暗示 Loomis 和 Whitney 的组合定理。