Weak difference property of functions with the Baire property

• Autorzy: Tamás Mátrai
• Języki publikacji: EN

Abstrakty

EN

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) ≠ 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.

Kategorie tematyczne

• 26A21: Classification of real functions; Baire classification of sets and functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 177
• Numer: 1
• Strony: 1-17

Daty

wydano

2003

Twórcy

autor

Tamás Mátrai

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

Identyfikatory

DOI

10.4064/fm177-1-1