%0 Journal Article
%T Bounded variation and the strength of Helly's selection theorem
%A Alexander P. Kreuzer
%J Mathematics
%D 2013
%I arXiv
%R 10.2168/LMCS-10(4:16)2014
%X We analyze the strength of Helly's selection theorem HST, which is the most important 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 the Bolzano-Weierstra\ss\ principle over RCA0. With this HST is equivalent to ACA0 over RCA0. A similar classification is obtained in the Weihrauch lattice.
%U http://arxiv.org/abs/1308.3881v5