Weak difference property of functions with the Baire property

Tamás Mátrai¹

¹ Department of Applied Analysis Eötvös Loránd University Pázmány Péter sétány 1//C 1117 Budapest, Hungary

Fundamenta Mathematicae, Tome 177 (2003) no. 1, pp. 1-17.

Résumé

We prove that the class of functions with the Baire property has the weak difference property in category sense. That is, every function for which $ f(x+h) - f(x)$ has the Baire property for every $h \in {\mathbb R} $ can be written in the form $ f = g +H + \phi $ where $g$ has the Baire property, $H$ is additive, and for every $h \in {\mathbb R} $ we have $ \phi (x+h) - \phi (x) \not =0 $ only on a meager set. We also discuss the weak difference property of some subclasses of the class of functions with the Baire property, and the consistency of the difference property of the class of functions with the Baire property.

Détail

DOI : 10.4064/fm177-1-1

Keywords: prove class functions baire property has weak difference property category sense every function which has baire property every mathbb written form phi where has baire property additive every mathbb have phi phi only meager set discuss weak difference property subclasses class functions baire property consistency difference property class functions baire property