1. Baire one functions and their sets of discontinuity
- Creator:
- Fenecios, Jonald P., Cabral, Emmanuel A., and Racca, Abraham P.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Baire class one function, set of points of discontinuity, and oscillation of a function
- Language:
- English
- Description:
- A characterization of functions in the first Baire class in terms of their sets of discontinuity is given. More precisely, a function f : R → R is of the first Baire class if and only if for each ε > 0 there is a sequence of closed sets {Cn}∞ n=1 such that Df = ∞S n=1 Cn and ωf (Cn) < ε for each n where ωf (Cn) = sup{|f(x) − f(y)|: x, y ∈ Cn} and Df denotes the set of points of discontinuity of f. The proof of the main theorem is based on a recent ε-δ characterization of Baire class one functions as well as on a wellknown theorem due to Lebesgue. Some direct applications of the theorem are discussed in the paper.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public