Search results for "Haar null"
showing 3 items of 3 documents
A remark on differentiable functions with partial derivatives in Lp
2004
AbstractWe consider a definition of p,δ-variation for real functions of several variables which gives information on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p,δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.
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.
A local notion of absolute continuity in IR^n
2005
We consider the notion of p, δ-absolute continuity for functions of several variables introduced in [2] and we investigate the validity of some basic properties that are shared by absolutely continuous functions in the sense of Maly. We introduce the class $δ−BV^p_loc(\Omega,IR^m)$ and we give a characterization of the functions belonging to this class.