A selection theorem for essentially regulated functions of several variables

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Helly's selection theorem provides a criterion for compactness of sets of single-variable functions with bounded pointwise variation. Fraňková has given a proper extension of Helly's theorem to the setting of single-variable regulated functions. We show how a similar approach yields a natural notion of regulated functions of several variables, together with an extension of the standard compactness criterion for multi-variable functions of bounded variation.

Original languageEnglish (US)
Article number128099
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - Jun 15 2024

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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