Some consequences of a kind of Hahn-Banach's theorem
Some constructions of strictly ergodic non-regular Toeplitz flows
We give a necessary and sufficient condition for a Toeplitz flow to be strictly ergodic. Next we show that the regularity of a Toeplitz flow is not a topological invariant and define the "eventual regularity" as a sequence; its behavior at infinity is topologically invariant. A relation between regularity and topological entropy is given. Finally, we construct strictly ergodic Toeplitz flows with "good" cyclic approximation and non-discrete spectrum.
Some continuity and approximation properties of a countable iterated function system.
Some continuity and measurability results on spaces of measures.
Some convergence theorems for HK-integral in locally convex spaces
We present some convergence theorems for the HK-integral of functions taking values in a locally convex space. These theorems are based on the concept of HK-equiintegrability.
Some dimensional results for a class of special homogeneous Moran sets
We construct a class of special homogeneous Moran sets, called -quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of , we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of homogeneous Moran sets to assume the minimum value, which expands earlier works.
Some examples of d-ideals and related Baire systems
Some extensions of an inequality of Vapnik and Chervonenkis.
Some extreme contractions on -spaces
Some Fine Properties of BV Functions on Wiener Spaces
In this paper we define jump set and approximate limits for BV functions on Wiener spaces and show that the weak gradient admits a decomposition similar to the finite dimensional case. We also define the SBV class of functions of special bounded variation and give a characterisation of SBV via a chain rule and a closure theorem. We also provide a characterisation of BV functions in terms of the short-time behaviour of the Ornstein-Uhlenbeck semigroup following an approach due to Ledoux.
Some fine properties of sets with finite perimeter in Wiener spaces
In this paper we give a brief overview on the state of art of developments of Geometric Measure Theory in infinite-dimensional Banach spaces. The framework is given by an abstract Wiener space, that is a separable Banach space endowed with a centered Gaussian measure. The focus of the paper is on the theory of sets with finite perimeter and on their properties; this choice was motivated by the fact that most of the good properties of functions of bounded variation can be obtained, thanks to coarea...
Some fixed point theorems and existence of weak solutions of Volterra integral equation under Henstock-Kurzweil-Pettis integrability
In this paper we examine the set of weakly continuous solutions for a Volterra integral equation in Henstock-Kurzweil-Pettis integrability settings. Our result extends those obtained in several kinds of integrability settings. Besides, we prove some new fixed point theorems for function spaces relative to the weak topology which are basic in our considerations and comprise the theory of differential and integral equations in Banach spaces.
Some full descriptive characterizations of the Henstock-Kurzweil integral in the Euclidean space
Using generalized absolute continuity, we characterize additive interval functions which are indefinite Henstock-Kurzweil integrals in the Euclidean space.
Some Functional Inequalities.
Some functionals on sets of stationary codes
Some generic properties of concentration dimension of measure
Let be a compact quasi self-similar set in a complete metric space and let denote the space of all probability measures on , endowed with the Fortet-Mourier metric. We will show that for a typical (in the sense of Baire category) measure in the lower concentration dimension is equal to , while the upper concentration dimension is equal to the Hausdorff dimension of .
Some limit ratio theorem related to a real endomorphism in case of a neutral fixed point
Some metric-singular properties of the graph of solutions of the one-dimensional -Laplacian.
Some new cases of realization of spectral multiplicity function for ergodic transformations
Some New Examples of Gibbs Measures.