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On almost continuous additive functions. (English) Zbl 0892.26004
It is proved that every additive function is the sum of two almost continuous (in Stallings’ sense) additive functions and the limit of a sequence (of a transfinite sequence) of almost continuous additive functions. Moreover, it is shown that the maximal additive family for the set of all almost continuous additive functions having the graphs of the second category is contained in the class of continuous additive functions.

MSC:
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
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References:
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