Coarea不等式

摘要：

本文的目的是提供一个自包含的证明一般情况下的coarea不等式，也被称为艾伦伯格不等式。结果是已知的，但我们不知道任何地方，证明将书面的所有细节。已知的证明是基于戴维斯的一个困难的结果。我们的证明是初等的，不使用戴维斯定理。相反，我们使用了一个优雅的论点，我们从纳扎罗夫通过MathOverflow学习。我们还得到了coarea不等式的一些推广。

英文摘要：

The aim of this paper is to provide a self-contained proof of a general case of the coarea inequality, also known as the Eilenberg inequality. The result is known, but we are not aware of any place that a proof would be written with all details. The known proof is based on a difficult result of Davies. Our proof is elementary and does not use Davies' theorem. Instead we use an elegant argument that we learned from Nazarov through MathOverflow. We also obtain some generalizations of the coarea inequality.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。