Absolutely continuous functions in Rn

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 Ln, differentiable almost everywhere and satisfies the formula on change of variables.  2004 Elsevier Inc. All rights reserved.