Bounded variation and the strength of Helly's selection theorem

摘要

We analyze the strength of Helly's selection theorem HST, whichis the most important compactness theorem on the space of functions of boundedvariation. For this we utilize a new representation of this space intermediatebetween $L_1$ and the Sobolev space W1,1, compatible with the, so called, weak* topology. We obtain that HST is instance-wise equivalent to theBolzano-Weierstraß principle over RCA0. With thisHST is equivalent to ACA0 over RCA0. Asimilar classification is obtained in the Weihrauch lattice.