Weak difference property of functions with the Baire property

Tamás Mátrai. "Weak difference property of functions with the Baire property." Fundamenta Mathematicae 177.1 (2003): 1-17. <http://eudml.org/doc/282808>.

@article{TamásMátrai2003,
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 ∈ 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.},
author = {Tamás Mátrai},
journal = {Fundamenta Mathematicae},
keywords = {Baire property; weak difference property; consistency},
language = {eng},
number = {1},
pages = {1-17},
title = {Weak difference property of functions with the Baire property},
url = {http://eudml.org/doc/282808},
volume = {177},
year = {2003},
}

TY - JOUR
AU - Tamás Mátrai
TI - Weak difference property of functions with the Baire property
JO - Fundamenta Mathematicae
PY - 2003
VL - 177
IS - 1
SP - 1
EP - 17
AB - 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.
LA - eng
KW - Baire property; weak difference property; consistency
UR - http://eudml.org/doc/282808
ER -