On the Measurability of Functions of Two Variables
On the measurability of real functions defined on product-spaces
On the measurability of sets of pairs of intersecting nonisotropic straight lines of type beta in the simply isotropic space
The measurable sets of pairs of intersecting non-isotropic straight lines of type and the corresponding densities with respect to the group of general similitudes and some its subgroups are described. Also some Crofton-type formulas are presented.
On the measure of measurable sets of integers
On the Mellin Transforms of Dirac’S Delta Function, The Hausdorff Dimension Function, and The Theorem by Mellin
Mathematics Subject Classification: 44A05, 46F12, 28A78We prove that Dirac’s (symmetrical) delta function and the Hausdorff dimension function build up a pair of reciprocal functions. Our reasoning is based on the theorem by Mellin. Applications of the reciprocity relation demonstrate the merit of this approach.
On the minima of functionals with linear growth
On the Minimal Convex Annulus of a Planar Convex Body.
On the permeability of submeasures on finite algebras
On the product of operator valued measures
On the Relations Between 2D and 3D Fractal Dimensions: Theoretical Approach and Clinical Application in Bone Imaging
The inner knowledge of volumes from images is an ancient problem. This question becomes complicated when it concerns quantization, as the case of any measurement and in particular the calculation of fractal dimensions. Trabecular bone tissues have, like many natural elements, an architecture which shows a fractal aspect. Many studies have already been developed according to this approach. The question which arises however is to know to which extent it is possible to get an exact determination of the...
On the rigidity of one-dimensional systems of contraction similitudes.
On the selector problems for the partitions of Polish spaces and for the compact-valued mappings
On the self-similar Jordan arcs admitting structure parametrization.
On the setwise convergence of sequences of measures.
On the singularities of convex functions.
On the strong maximal function and rearrangements
On the structure of the intersection of two middle third Cantor sets.
Motivated by the study of planar homoclinic bifurcations, in this paper we describe how the intersection of two middle third Cantor sets changes as the sets are translated across each other. The resulting description shows that the intersection is never empty; in fact, the intersection can be either finite or infinite in size. We show that when the intersection is finite then the number of points in the intersection will be either 2n or 3 · 2n. We also explore the Hausdorff dimension of the intersection...
On the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces
On the theorem of Ivasev-Musatov. I
We give a new version of Ivasev-Musatov’s construction of a measure whose support has Lebesgue measure zero but whose Fourier transform drops away extremely rapidly.
On the theorem of Ivasev-Musatov. II
As in Part I [Annales de l’Inst. Fourier, 27-3 (1997), 97-113], our object is to construct a measure whose support has Lebesgue measure zero, but whose Fourier transform drops away extremely fast.