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SOLUTIONS OF A GOŁA̧B–SCHINZEL-TYPE FUNCTIONAL EQUATION BOUNDED ON ‘BIG’ SETS IN AN ABSTRACT SENSE

Part of: Miscellaneous topics in measure theory

Published online by Cambridge University Press:  05 March 2010

ELIZA JABŁOŃSKA
ELIZA JABŁOŃSKA*
Affiliation:
Department of Mathematics, Rzeszów University of Technology, W. Pola 2, 35-959 Rzeszów, Poland (email: elizapie@prz.edu.pl)
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Abstract

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It is well known that an exponential real function, which is Lebesgue measurable (Baire measurable, respectively) or bounded on a set of positive Lebesgue measure (of the second category with the Baire property, respectively), is continuous. Here we consider bounded on ‘big’ set solutions of an equation generalizing the exponential equation as well as the Goła̧b–Schinzel equation. Moreover, we unify results into a more general and abstract case.

Keywords

Baire categoryLebesgue measurabilityGoła̧b–Schinzel equationexponential functionbounded solutions

MSC classification

Secondary: 28E05: Nonstandard measure theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 3 , June 2010 , pp. 430 - 441
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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