In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and we characterise the minimal weak upper gradient of all Lipschitz functions.

中文翻译：

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加权欧几里得空间上高梯度的刻画及其应用

在配备任意Radon测度的欧几里得空间的背景下，我们证明了文献中存在的Sobolev空间的几种不同概念之间的等价关系，并且我们刻画了所有Lipschitz函数的最小弱上坡。