Geodesic
Classifications and characterizations of Baire-1 functions
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 4, pp. 733-748

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Kechris and Louveau in [5] classified the bounded Baire-1 functions, which are defined on a compact metric space $K$, to the subclasses $\Cal B_{1}^{\xi }(K)$, $\xi \omega_1$. In [8], for every ordinal $\xi \omega_{1}$ we define a new type of convergence for sequences of real-valued functions ($\xi $-uniformly pointwise) which is between uniform and pointwise convergence. In this paper using this type of convergence we obtain a classification of pointwise convergent sequences of continuous real-valued functions defined on a compact metric space $K$, and also we give a characterization of the classes $\Cal B_{1}^{\xi }(K)$, $1 \leq \xi \omega_{1}$.
Classification : 46E99, 54C30, 54C35, 54C50
Keywords: Baire-1 functions; convergence index; oscillation index; trees 
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     title = {Classifications and characterizations of {Baire-1} functions},
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Kiriakouli, P. Classifications and characterizations of Baire-1 functions. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 4, pp. 733-748. http://geodesic.mathdoc.fr/item/CMUC_1998__39_4_a8/