Shu Takeuchi

The pointed intrinsic flat distance between locally integral current spaces

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.