Kreuzer, Alexander P. - Bounded variation and the strength of Helly's selection theorem

lmcs:980 - Logical Methods in Computer Science, December 24, 2014, Volume 10, Issue 4
Bounded variation and the strength of Helly's selection theorem

Authors: Kreuzer, Alexander P.

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.


Source : oai:arXiv.org:1308.3881
DOI : 10.2168/LMCS-10(4:16)2014
Volume: Volume 10, Issue 4
Published on: December 24, 2014
Submitted on: June 25, 2015
Keywords: Mathematics - Logic,Computer Science - Logic in Computer Science


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