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A characterization of functions in the first Baire class in terms of their sets of discontinuity is given. More precisely, a function is of the first Baire class if and only if for each there is a sequence of closed sets such that and for each where
and denotes the set of points of discontinuity of . The proof of the main theorem is based on a recent - characterization of Baire class one functions as well as on a well-known theorem due to Lebesgue. Some direct applications of...
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