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.

• 03B30 - Foundations of classical theories (including reverse mathematics)
• 03D30 - Other degrees and reducibilities in computability and recursion theory
• 03F35 - Second- and higher-order arithmetic and fragments

• 1 zbMATH Open