Topological Markov chains with dicyclic dimension group.
Topological Pressure for One-Dimensional Holomorphic Dynamical Systems
For a class of one-dimensional holomorphic maps f of the Riemann sphere we prove that for a wide class of potentials φ the topological pressure is entirely determined by the values of φ on the repelling periodic points of f. This is a version of a classical result of Bowen for hyperbolic diffeomorphisms in the holomorphic non-uniformly hyperbolic setting.
Topological properties of generalized Wallman spaces and lattice relations.
Topological Properties of the Additon Map in Spaces of Borel Measures.
Topological properties of two-dimensional number systems
In the two dimensional real vector space one can define analogs of the well-known -adic number systems. In these number systems a matrix plays the role of the base number . In the present paper we study the so-called fundamental domain of such number systems. This is the set of all elements of having zero integer part in their “-adic” representation. It was proved by Kátai and Környei, that is a compact set and certain translates of it form a tiling of the . We construct points, where...
Topological rings of sets and the theory of vector measures [Book]
Topological spaces admitting a unique fractal structure
Each homeomorphism from the n-dimensional Sierpiński gasket into itself is a similarity map with respect to the usual metrization. Moreover, the topology of this space determines a kind of Haar measure and a canonical metric. We study spaces with similar properties. It turns out that in many cases, "fractal structure" is not a metric but a topological phenomenon.
Topological spaces with the strong Skorokhod property.
Topologies on measure spaces and the Radon-Nikodym theorem
Topologies on Spaces of Vector-Valued Continuous Functions. II.
Towers of measurable functions
We formulate variants of the cardinals f, p and t in terms of families of measurable functions, in order to examine the effect upon these cardinals of adding one random real.
Traces of Besov spaces on fractal h-sets and dichotomy results
We study the existence of traces of Besov spaces on fractal h-sets Γ with a special focus on assumptions necessary for this existence; in other words, we present criteria for the non-existence of traces. In that sense our paper can be regarded as an extension of Bricchi (2004) and a continuation of Caetano (2013). Closely connected with the problem of existence of traces is the notion of dichotomy in function spaces: We can prove that-depending on the function space and the set Γ-there occurs an...
Traces of Oscillating Functions.
Trägertopologien auf meßbaren Räumen.
Transfinite inductions producing coanalytic sets
A. Miller proved the consistent existence of a coanalytic two-point set, Hamel basis and MAD family. In these cases the classical transfinite induction can be modified to produce a coanalytic set. We generalize his result formulating a condition which can be easily applied in such situations. We reprove the classical results and as a new application we show that consistently there exists an uncountable coanalytic subset of the plane that intersects every C¹ curve in a countable set.
Transformation d'une promesure de probabilité en une vraie mesure
Transformations cylindriques et mesures finies invariantes
Transformations preserving the Hausdorff-Besicovitch dimension
Continuous transformations preserving the Hausdorff-Besicovitch dimension (“DP-transformations”) of every subset of R 1 resp. [0, 1] are studied. A class of distribution functions of random variables with independent s-adic digits is analyzed. Necessary and sufficient conditions for dimension preservation under functions which are distribution functions of random variables with independent s-adic digits are found. In particular, it is proven that any strictly increasing absolutely continuous distribution...
Transforms of Vector-Valued Functions and Measures
Transport de mesure et courbures de Ricci synthétiques dans le groupe de Heisenberg
Dans ces notes il sera expliqué que la propriété est vérifiée par le groupe de Heisenberg muni de la distance de Carnot-Carathéodory et de la mesure de Lebesgue. Cette propriété correspond pour les espaces métriques mesurés à une courbure de Ricci positive. Comme application, les mesures interpolées par transport de mesure sont absolument continues. En revanche, la courbure-dimension , une autre courbure de Ricci synthétique adaptée aux espaces métriques mesurés est fausse pour .