Baire one star function

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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).

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