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On pointwise limits of sequences of I-continuous functions. (English) Zbl 0613.26004
In the paper, the family $$B_ 1({\mathcal C}_ I)$$ of pointwise limits of sequences of I-continuous functions is considered. We formulate a condition necessary for a function to be in $$B_ 1({\mathcal C}_ I)$$, analogous to that given by Z. Grande. Moreover, we show that $$B_ 1({\mathcal C}_ I)$$ essentially contains the Baire class 1 and is essentially contained in the Baire class 2.
##### MSC:
 26A21 Classification of real functions; Baire classification of sets and functions 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) 28A05 Classes of sets (Borel fields, $$\sigma$$-rings, etc.), measurable sets, Suslin sets, analytic sets
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