Topological Dynamics of Transformations Induced on the Space of Probability Measures.
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