# zbMATH — the first resource for mathematics

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