Source: Real Anal. Exchange Volume 34, Number 1
(2008), 29-48.
We give a new characterization of the Baire class $1$ functions (defined on an ultrametric space) by proving that they are exactly the pointwise limits of sequences of full functions, which are particularly simple Lipschitz functions. Moreover we highlight the link between the two classical stratifications of the Borel functions by showing that the Baire class functions of some level are exactly those obtained as uniform limits of sequences of Delta functions of a corresponding level.
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References
A. S. Kechris, Classical descriptive set theory, Grad. Texts in Math., 156 Springer-Verlag, Heidelberg, New York, 1995.
A. S. Kechris and A. Louveau, A classification of Baire class $1$ functions, Trans. Amer. Math. Soc. 318 (1990), no. 1, 209–236.
Mathematical Reviews (MathSciNet):
MR946424
P. Kiriakoui, A classification of Baire-$1$ functions, Trans. Amer. Math. Soc. 351 (1999), 4599–4609.
R. Haydon, E. Odell and H. P. Rosenthal, Certain subclasses of Baire-$1$ functions with Banach space applications, Longhorn Notes, University of Texas at Austin Functional Analysis Seminar (1987–89).
H. P. Rosenthal, A characterization of Banach spaces containing $c_0$, J. Amer. Math. Soc. 7 (1994), 707–748.
S. Solecki, Decomposing Borel sets and functions and the structure of Baire class 1 functions, J. Amer. Math. Soc. 11 (1998), no. 3, 521–550.