The Hausdorff a-Dimensional Measures of the Level Sets and the Graph of the TV-Parameter Wiener Process.
The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping.
The Hausdorff dimension of some special plane sets
A compact set is constructed such that each horizontal or vertical line intersects in at most one point while the -dimensional measure of is infinite for every .
The Hausdorff dimension of the projections of self-affine carpets
We study the orthogonal projections of a large class of self-affine carpets, which contains the carpets of Bedford and McMullen as special cases. Our main result is that if Λ is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of Λ in a non-principal direction has Hausdorff dimension min(γ,1), where γ is the Hausdorff dimension of Λ. This generalizes a recent result of Peres and Shmerkin on sums of Cantor sets.
The Hausdorff lower semicontinuous envelope of the length in the plane
We study the Hausdorff lower semicontinuous envelope of the length in the plane. This envelope is taken with respect to the Hausdorff metric on the space of the continua. The resulting quantity appeared naturally as the rate function of a large deviation principle in a statistical mechanics context and seems to deserve further analysis. We provide basic simple results which parallel those available for the perimeter of Caccioppoli and De Giorgi.
The Henstock-Kurzweil approach to Young integrals with integrators in
In 1938, L. C. Young proved that the Moore-Pollard-Stieltjes integral exists if , and . In this note we use the Henstock-Kurzweil approach to handle the above integral defined by Young.
The Henstock-Kurzweil-Pettis integrals and existence theorems for the Cauchy problem
In this paper we prove an existence theorem for the Cauchy problem using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function satisfies some conditions expressed in terms of measures of weak noncompactness.
The homology of spaces of simple topological measures
The simple topological measures X* on a q-space X are shown to be a superextension of X. Properties inherited from superextensions to topological measures are presented. The homology groups of various subsets of X* are calculated. For a q-space X, X* is shown to be a q-space. The homology of X* when X is the annulus is calculated. The homology of X* when X is a more general genus one space is investigated. In particular, X* for the torus is shown to have a retract homeomorphic to an infinite product...
The Horocycle Flow is Mixing of all Degrees.
The ideal (a) is not generated
We prove that the ideal (a) defined by the density topology is not generated. This answers a question of Z. Grande and E. Strońska.
The inner structure of real extensors in uniform spaces
The integral analog of a series with a two-point sum range.
The invariance principle for nonstationary sequences of associated random variables
The Jordan decomposition of the null-additive signed fuzzy measures.
The Kantorovich metric: the initial history and little-known applications.
The Kantorovič-Rubinstein distance
The Kantorovič-Rubinstein distance
The kernel operation on subsets of a -space
The Kluvanek-Kantorovitz characterization of scalar operators in locally convex spaces.
The Kurzweil construction of an integral in ordered spaces
This paper generalizes the results of papers which deal with the Kurzweil-Henstock construction of an integral in ordered spaces. The definition is given and some limit theorems for the integral of ordered group valued functions defined on a Hausdorff compact topological space with respect to an ordered group valued measure are proved in this paper.