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 ...

We study the functions whose composition with Baire class one functions are Baire class one functions. We first prove some characterizations of such functions, then investigate a subclass of such functions which are defined in a natural way.

This note is about functions f : Aω → Bω whose graph is recognized by a Büchi finite automaton on the product alphabet A×B. These functions are Baire class 2 in the Baire hierarchy of Borel functions and it is decidable whether such fonction are continuous or not. In 1920 W. Sierpinski showed that a function f : R → R is Baire class 1 if and only if both the overgraph and the undergraph of f ar...

We discuss the connection of additive set functions to dual function spaces by means of integrals. Isometrical isomorphisms are presented between: a) bounded contents and the dual of uniformly approximable functions, b) charges on Baire algebras and the duals of bounded, continuous functions over A-topological spaces, c) Hewitt measures on Baire σ-algebras and the duals of continuous functions ...