Absolute upper semicontinuity
Copyright policy )Absolute upper semicontinuity
It is proved that the following conditions are equivalent: the function ϕ [a, b]→R is absolutely upper semicontinuous (see [1]); ϕ is a function of bounded variation with decreasing singular part; there exists a summable function g: [a, b] → R such that for anyt′∈[a, b] andt″∈[t′, b], we have ϕ(t″)−ϕ(t′)⩽∫ t′ t″ g (s) ds.
- University of Latvia Latvia
functions of bounded variation, differential inequality, Functions of bounded variation, generalizations, Differential inequalities involving functions of a single real variable, Inequalities involving derivatives and differential and integral operators, absolutely upper semicontinuous functions, Absolutely continuous real functions in one variable
functions of bounded variation, differential inequality, Functions of bounded variation, generalizations, Differential inequalities involving functions of a single real variable, Inequalities involving derivatives and differential and integral operators, absolutely upper semicontinuous functions, Absolutely continuous real functions in one variable
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