Hellenica World

.

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).