In this note, we define a distance between two pointed locally integral current spaces. We prove that a sequence of pointed locally integral current spaces converges with respect to this distance if and only if it converges in the sense of Lang–Wenger. This enables us to state the compactness theorem by Lang–Wenger for pointed locally integral current spaces in terms of a distance function.

中文翻译：

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局部积分电流空间之间的尖锐固有平面距离

在本笔记中，我们定义了两个指向的局部积分电流空间之间的距离。我们证明了一系列指向局部积分的电流空间关于这个距离收敛当且仅当它在 Lang-Wenger 的意义上收敛。这使我们能够根据距离函数来陈述 Lang-Wenger 的紧凑性定理，用于指向局部积分电流空间。