A quantitative version of Helly’s selection principle in Banach spaces and its applications


We present a novel generalization, in Banach spaces, of the celebrated Helly’s principle selection. Specifically, our main result is a quantitative version of such principle selection. Our main tool is the so called Degree of Nondensifiability, which measures (in the specified sense) the distance of a given convex subset of a Banach space to the class of its Peano Continua. As application of our results, we analyze the solvability of certain Volterra integral equations.

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Correspondence to G. García.

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Communicated by Constantin Niculescu.

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García, G. A quantitative version of Helly’s selection principle in Banach spaces and its applications. Ann. Funct. Anal. (2020). https://doi.org/10.1007/s43034-020-00083-9

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  • Helly’s selection principle
  • Degree of Nondensifiability
  • \(\alpha \)-dense curves
  • Bochner integrals
  • Volterra integral equations

Mathematics Subject Classification

  • 26A45
  • 46B50
  • 46G12
  • 45D05
  • 40A10