Variations on lusin’s theorem

Jack B. Brown, Karel Prikry

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

We prove a theorem about continuous restrictions of Marczewski measurable functions to large sets. This theorem is closely related to the theorem of Lusin about continuous restrictions of Lebesgue measurable functions to sets of positive measure and the theorem of Nikodym and Kuratowski about continuous restrictions of functions with the Baire property (in the wide sense) to residual sets. This theorem is used to establish Lusin-type theorems for universally measurable functions and functions which have the Baire property in the restricted sense. The theorems are shown (under assumption of the Continuum Hypothesis) to be “best possible” within a certain context.

Original languageEnglish (US)
Pages (from-to)77-86
Number of pages10
JournalTransactions of the American Mathematical Society
Volume302
Issue number1
DOIs
StatePublished - Jul 1987

Keywords

  • Baire property
  • Blumberg’s theorem
  • Lusin’s theorem
  • Marczewski measurable. Both authors supported in part by grants from the National Science Foundation

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