Light side of compactness in Lebesgue spaces: Sudakov theorem

Przemysław Górka, Humberto Rafeiro

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


In this note we show that, in the case of bounded sets in metric spaces with some additional structure, the boundedness of a family of Lebesgue p-summable functions follow from a certain uniform limit norm condition. As a byproduct, the well known Riesz-Kolmogorov compactness theorem can be formulated only with one condition.

Original languageEnglish
Pages (from-to)135-139
Number of pages5
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Issue number1
Publication statusPublished - 2017
Externally publishedYes


  • Compactness
  • Metric measure spaces
  • Riesz-Kolmogorov theorem

ASJC Scopus subject areas

  • General Mathematics


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