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Sibirsk. Mat. Zh., 2004, Volume 45, Number 1, Pages 178–188 (Mi smj1057)  

Function decompositions related to the Luzin $N$-property

F. S. Nasyrov

Ufa State Aviation Technical University

Abstract: We introduce a class of continuous completely regular functions satisfying the $N$-property. We obtain a decomposition of an arbitrary continuous function into the sum of two functions the first of which is completely regular and the second does not enjoy the $N$-property. We define a class of strongly regular Borel functions for which we prove the Luzin $N$-property. We demonstrate that the image of every Lebesgue measurable set of a strongly regular function is measurable. From an arbitrary Borel function we extract a strongly regular function and a function that does not enjoy the $N$-property.

Keywords: Luzin $N$-property, distribution of a function, generalized local time, monotone rearrangement of a function

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English version:
Siberian Mathematical Journal, 2004, 45:1, 146–154

Bibliographic databases:

UDC: 517.2
Received: 20.02.2003

Citation: F. S. Nasyrov, “Function decompositions related to the Luzin $N$-property”, Sibirsk. Mat. Zh., 45:1 (2004), 178–188; Siberian Math. J., 45:1 (2004), 146–154

Citation in format AMSBIB
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\paper Function decompositions related to the Luzin $N$-property
\jour Sibirsk. Mat. Zh.
\yr 2004
\vol 45
\issue 1
\pages 178--188
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2048761}
\zmath{https://zbmath.org/?q=an:1054.26004}
\transl
\jour Siberian Math. J.
\yr 2004
\vol 45
\issue 1
\pages 146--154
\crossref{https://doi.org/10.1023/B:SIMJ.0000013020.30432.7e}
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