Generalized Vitali systems of uniform type
Gradients of Borel functions
Halbborelsche Funktionen und extreme Ableitungen
Hölder quasicontinuity of Sobolev functions on metric spaces.
We prove that every Sobolev function defined on a metric space coincides with a Hölder continuous function outside a set of small Hausdorff content or capacity. Moreover, the Hölder continuous function can be chosen so that it approximates the given function in the Sobolev norm. This is a generalization of a result of Malý [Ma1] to the Sobolev spaces on metric spaces [H1].
Integral functionals determined by their minima
Józef Marcinkiewicz (1910-1940) - on the centenary of his birth
Józef Marcinkiewicz’s (1910-1940) name is not known by many people, except maybe a small group of mathematicians, although his influence on the analysis and probability theory of the twentieth century was enormous. This survey of his life and work is in honour of the anniversary of his birth and anniversary of his death. The discussion is divided into two periods of Marcinkiewicz’s life. First, 1910-1933, that is, from his birth to his graduation from the University of Stefan Batory in Vilnius,...
Lebesgue points in variable exponent spaces.
Les dérivations analytiques
Measurability of multifunctions of two variables [Book]
Measure and category versions of Erdős-Rado theorem.
Mesures cylindriques singulières sur un espace de Hilbert. Équivalence et orthogonalité
Note on differentiation of integrals and the halo conjecture
Note on generalized multiple Perron integral
On a characterization of quasicontinuous multifunctions
On compact embedding theorems in weighted Sobolev spaces
On differential bases formed of intervals.
On differentiation of integrals with respect to bases of convex sets.
Differentiation of integrals of functions from the class with respect to the basis of convex sets is established. An estimate of the rate of differentiation is given. It is also shown that there exist functions in , N ≥ 3, and with ω(δ)/δ → ∞ as δ → +0 whose integrals are not differentiated with respect to the bases of convex sets in the corresponding dimension.
On essential cluster sets
On strong differentiability of integrals along different directions.
On submeasures. II.