RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Sibirsk. Mat. Zh.: Year: Volume: Issue: Page: Find

 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

Full text: PDF file (200 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.2

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
\Bibitem{Nas04} \by F.~S.~Nasyrov \paper Function decompositions related to the Luzin $N$-property \jour Sibirsk. Mat. Zh. \yr 2004 \vol 45 \issue 1 \pages 178--188 \mathnet{http://mi.mathnet.ru/smj1057} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000189126800013}