### 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 language | English (US) |
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Pages (from-to) | 77-86 |

Number of pages | 10 |

Journal | Transactions of the American Mathematical Society |

Volume | 302 |

Issue number | 1 |

DOIs | |

State | Published - 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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## Cite this

Brown, J. B., & Prikry, K. (1987). Variations on lusin’s theorem.

*Transactions of the American Mathematical Society*,*302*(1), 77-86. https://doi.org/10.1090/S0002-9947-1987-0887497-6