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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Variations on Lusin's theorem


Authors: Jack B. Brown and Karel Prikry
Journal: Trans. Amer. Math. Soc. 302 (1987), 77-86
MSC: Primary 26A15; Secondary 28A20, 54C30
MathSciNet review: 887497
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0887497-6
PII: S 0002-9947(1987)0887497-6
Keywords: Lusin's theorem, Blumberg's theorem, Baire property, Marczewski measurable
Article copyright: © Copyright 1987 American Mathematical Society