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Oscillation and \(\omega\)-primitives. (English) Zbl 1025.26002
The authors investigate topological spaces \(X\) such that for upper semicontinuous functions \(f:X \to [0,\infty)\) (or \(f:X \to [0,\infty ]\)) there are \(\omega \)-primitives \(F:X \to [0,\infty)\) (or \(F:X \to [0,\infty ]\)) whose oscillations equal \(f\) on \(X\). Moreover, convergences of sequences of \(\omega\)-primitives are discussed.

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