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.
BONGIORNO D (2005). Absolutely continuous functions in R-n. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 303(1), 119-134 [10.1016/j.jmaa.2004.08.002].
Absolutely continuous functions in R-n
BONGIORNO, Donatella
2005-01-01
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.
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