Variations on Lusin’s theorem
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- by Jack B. Brown and Karel Prikry PDF
- Trans. Amer. Math. Soc. 302 (1987), 77-86 Request permission
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.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 302 (1987), 77-86
- MSC: Primary 26A15; Secondary 28A20, 54C30
- DOI: https://doi.org/10.1090/S0002-9947-1987-0887497-6
- MathSciNet review: 887497