Title: Equality of the usual definitions of Brakke flow,
Abstract: In 1978 Brakke introduced the mean curvature flow in the setting of geometric
measure theory. There exist multiple variants of the original definition. Here
we prove that most of them are indeed equal. One central point is to correct
the proof of Brakke's §3.5, where he develops an estimate for the evolution
of the measure of time-dependent test functions.