A Baire one star function is a type of function studied in real analysis.
, and is called a Baire one star function if, for each perfect set
The notion seems to have originated with B. Kirchheim in an article titled 'Baire one star functions' (Real Anal.
The terminology is actually due to Richard O'Malley, 'Baire* 1, Darboux functions' Proc.
See H. W. Ellis, 'Darboux properties and applications to nonabsolutely convergent integrals' Canad.
J., 3 (1951), 471–484, where the same concept is labelled as [CG] (for generalized continuity).
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