Comparison of Some Subfamilies of Functions Having The Baire Property

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Weak difference property of functions with the Baire property

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 ∈ R can be written in the form f = g+H+φ where g has the Baire property, H is additive, and for every h ∈ R we have φ(x+h)−φ(x) 6= 0 only on a meager set. We also discuss the weak difference property of ...

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ژورنال

عنوان ژورنال: Tatra Mountains Mathematical Publications

سال: 2016

ISSN: 1210-3195

DOI: 10.1515/tmmp-2016-0013