episciences.org_980_1638767852
1638767852
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Logical Methods in Computer Science
1860-5974
12
24
2014
Volume 10, Issue 4
Bounded variation and the strength of Helly's selection theorem
Alexander P.
Kreuzer
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.
12
24
2014
980
arXiv:1308.3881
10.2168/LMCS-10(4:16)2014
https://lmcs.episciences.org/980