Open Access
2005-2006 Relationships between continuity and abstract measurability of functions.
Artur Bartoszewicz, Elżbieta Kotlicka
Author Affiliations +
Real Anal. Exchange 31(1): 73-96 (2005-2006).


Making use of ideas of Marczewski and Sierpinski we propose a general approach to studies on connections between measurability, continuity and relative continuity of functions. Theorem 2.1 shows that a well-known characterization of $(s)$-measurable Marczewski functions can be extended to the case of functions measurable with respect to a wide class of algebras involved with a topology. Theorem 2.2 gene\-ralizes the Denjoy-Stepanoff theorem and shows that the Denjoy-Stepanoff property stating the continuity of $\mc A$-measurable functions at all points of a co-negligible set is quite common while an algebra $\mc A$ and an ideal $\mc J$ are the results of operations $S$ and $S_0$ on $\tau\setminus\mc I$ for a given topology $\tau$. Also from the obtained results we conclude new theorems concerning the algebras associated with product ideals (Theorems \ref{t320} and \ref{t310}).


Download Citation

Artur Bartoszewicz. Elżbieta Kotlicka. "Relationships between continuity and abstract measurability of functions.." Real Anal. Exchange 31 (1) 73 - 96, 2005-2006.


Published: 2005-2006
First available in Project Euclid: 5 June 2006

zbMATH: 1107.28001
MathSciNet: MR2218190

Primary: 03E15 , 03E20 , 28A05 , 54H05

Keywords: Denjoy-Stepanoff theorem , density-type topologies , MB-representation , measurability , relative continuity

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 1 • 2005-2006
Back to Top