Baire one star function is a term from real analysis. A function
f
:
R
→
R
is in class Baire* one, written
f
∈
B
1
∗
, and is called a Baire one star function, if for each perfect set
P
∈
R
, there is an open interval
I
∈
R
, such that
P
∩
I
is nonempty, and the restriction
f
|
P
∩
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).
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 [CG] (for generalized continuity).
