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arXiv · 1308.3881

Bounded variation and the strength of Helly's selection theorem

Alexander P. Kreuzer
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Abstract

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-Weierstraß principle over RCA0. With this HST is equivalent to ACA0 over RCA0. A similar classification is obtained in the Weihrauch lattice.

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BibTeXRIS

Alexander P. Kreuzer. 2014-12-23. Bounded variation and the strength of Helly's selection theorem. https://doi.org/10.2168/lmcs-10(4%3A16)2014

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