234:. The notion seems to have originated with B. Kirchheim in an article titled 'Baire one star functions' (Real Anal. Exch. 18 (1992/93), 385–399). The terminology is actually due to Richard O'Malley, 'Baire* 1, Darboux functions' Proc. Amer. Math. Soc. 60 (1976), 187–192. The concept itself (under a different name) goes back at least to 1951. See H. W. Ellis, 'Darboux properties and applications to nonabsolutely convergent integrals' Canad. Math. J., 3 (1951), 471–484, where the same concept is labelled as (for generalized continuity).
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