# .

# Baire one star function

Baire one star function is a term from real analysis. A function \(f: \mathbb{R} \to \mathbb{R} \) is in class Baire* one, written \( f \in \mathbf{B}^{*}_{1} \), and is called a Baire one star function, if for each perfect set P \in \mathbb{R}, there is an open interval \( I \in \mathbb{R} \), such that \( P \cap I \) is nonempty, and the restriction \( f |_{P \cap I} \) is continuous. The notion seems to have originated with B. Kerchheim in an article titled 'Baire one star functions' (Real Anal. Exch. 18 (1992/93), 385-399).

External links

A paper which defines class Baire* one

Retrieved from "http://en.wikipedia.org/"

All text is available under the terms of the GNU Free Documentation License