Search results for "Quasi-continuous function"

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A remark on absolutely continuous functions in ℝ n

2006

We introduce the notion ofα, λ-absolute continuity for functions of several variables and we compare it with the Hencl’s definition. We obtain that eachα, λ-absolutely continuous function isn, λ-absolutely continuous in the sense of Hencl and hence is continuous, differentiable almost everywhere and satisfies change of variables results based on a coarea formula and an area formula.

Discrete mathematicsChange of variablesContinuous functionGeneral MathematicsAlmost everywhereQuasi-continuous functionCoarea formulaDifferentiable functionAlgebra over a fieldAbsolute continuityMathematicsRendiconti del Circolo Matematico di Palermo
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Absolutely continuous functions in Rn

2005

Abstract For each 0 α 1 we consider a natural n-dimensional extension of the classical notion of absolute continuous function. We compare it with the Malý's and Hencl's definitions. It follows that each α-absolute continuous function is continuous, weak differentiable with gradient in L n , differentiable almost everywhere and satisfies the formula on change of variables.

Polish groupPure mathematicsChange of variablesα-regular intervalsContinuous functionApplied MathematicsMathematical analysisNull set or empty setQuasi-continuous functionAbsolute continuityWeak derivativeAbsolutely continuous functionsSobolev spaceHaar nullSobolev spacesAlmost everywhereDifferentiable functionAnalysisMathematicsJournal of Mathematical Analysis and Applications
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