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Abstract

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.