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On some representations of a.e. continuous functions. (English) Zbl 0851.26003

Summary: It is proved that the following conditions are equivalent:
(a) \(f\) is an almost everywhere continuous function.
(b) \(f = g + h\), where \(g,h\) are strongly quasi-continuous.
(c) \(f = c + gh\), where \(c \in \mathbb{R}\) and \(g,h\) are strongly quasi-continuous.

MSC:

26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
54C08 Weak and generalized continuity
54C30 Real-valued functions in general topology
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