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Baire-1 functions; convergence index; oscillation index; trees
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 $\Cal B_{1}^{\xi }(K)$, $1 \leq \xi < \omega_{1}$.
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