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Bounded variation and the strength of Hellys selection theorem

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 نشر من قبل Alexander P. Kreuzer
 تاريخ النشر 2013
  مجال البحث الهندسة المعلوماتية
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We analyze the strength of Hellys 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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