Bounded variation and the strength of Helly's selection theorem

We analyze the strength of Helly's selection theorem HST, which is the mostimportant compactness theorem on the space of functions of bounded variation.For this we utilize a new representation of this space intermediate between$L_1$ and the Sobolev space W1,1, compatible with the, so called, weak*topology. We obtain that HST is instance-wise equivalent to theBolzano-Weierstra\ss\ principle over RCA0. With this HST is equivalent to ACA0over RCA0. A similar classification is obtained in the Weihrauch lattice