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

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