In the existing language for tensor calculus on RCD spaces, tensor fields are only defined \(\mathfrak {m}\)-a.e.. In this paper we introduce the concept of tensor field defined ‘2-capacity-a.e.’ and discuss in which sense Sobolev vector fields have a 2-capacity-a.e. uniquely defined quasi-continuous representative.

中文翻译：

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RCD空间上的准连续向量场

在RCD空间上的张量微积分的现有语言中，仅定义了张量字段\（\ mathfrak {m} \）- ae。在本文中，我们介绍了定义“ 2-capacity-ae”的张量场的概念，并讨论了在哪种意义上Sobolev向量场具有“ 2-capacity-ae”唯一定义的准连续代表。