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RESEARCH PRODUCT

Absolutely continuous functions in Rn

Donatella Bongiorno

subject

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

description

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.

yearjournalcountryeditionlanguage
2005-03-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2004.08.002