Darboux property for functions of several variables
Defects and transformations of quasi-copulas
Six different functions measuring the defect of a quasi-copula, i. e., how far away it is from a copula, are discussed. This is done by means of extremal non-positive volumes of specific rectangles (in a way that a zero defect characterizes copulas). Based on these defect functions, six transformations of quasi-copulas are investigated which give rise to six different partitions of the set of all quasi-copulas. For each of these partitions, each equivalence class contains exactly one copula being...
Denseness of domains of differential operators in Sobolev spaces.
Differentiability of Minima of Non-Differentiable Functionals.
Differentiation bases for Sobolev functions on metric spaces.
We study Lebesgue points for Sobolev functions over other collections of sets than balls. Our main result gives several conditions for a differentiation basis, which characterize the existence of Lebesgue points outside a set of capacity zero.
Dvoretzky Theorem - Thirty Years Later (Survey).