From Arzelà–Ascoli to Riesz–Kolmogorov

Przemysław Górka, Humberto Rafeiro

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


In this paper we study totally bounded sets in Banach function spaces (BFS), from which we characterize compact sets (via Hausdorff criterion) in some non-standard function spaces which fall under the umbrella of BFS. We obtain a Riesz–Kolmogorov compactness theorem for the grand variable exponent Lebesgue spaces.

Original languageEnglish
Pages (from-to)23-31
Number of pages9
JournalNonlinear Analysis, Theory, Methods and Applications
Publication statusPublished - Oct 1 2016
Externally publishedYes


  • Banach function spaces
  • Grand variable exponent Lebesgue spaces
  • Metric measure spaces
  • Riesz–Kolmogorov theorem

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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