It is well known that BV([0, T]; X) satisfies the compactness theorem known as Helly's selection theorem: given any sequence of functions (fn)n∈N in BV([0, T]; X) that is uniformly bounded in the total variation norm, there exists a subsequence
BV([0, T]; X) is well-known to satisfy Helly's selection theorem: for any sequence of functions (fn)n∈N within BV([0, T]; X), if they are uniformly bounded in terms of total variation, then there is a subsequence that converges.