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A Haar meager set that is not strongly Haar meager
Following Darji, we say that a Borel subset B of an abelian Polish group G is Haar meager if there is a compact metric space K and a continuous...
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K -subadditive andK -superadditive set-valued functions bounded on “large” setsWe prove that every K –subadditive set–valued map weakly K –upper bounded on a “large” set (e.g. not null–finite, not Haar–null or not a Haar–meager...
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Further remarks on local K-boundedness of K-subadditive set-valued maps
Let X be an abelian metric group with an invariant metric, Y be a real normed space and K be a convex cone in Y . We prove that a K -subadditive ( K -supe...
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Hermitian Metrics on the Resolvent Set
For elements \(A_1, \ldots , A_n\) in a unital Banach algebra...
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Another approach to K-subadditivity
In the paper the notion of weakly K -subadditive set-valued maps is introduced in such a way that F is weakly K -superadditive if and only if
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On bounded paradoxical sets and Lie groups
We will prove that any non-empty open set in every complete connected metric space ( X , d ), where balls have compact closures, contains a paradoxical...
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Null-finite sets in topological groups and their applications
In the paper we introduce and study a new family of “small” sets which is tightly connected with two well known σ -ideals: of Haar-null sets and of...
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Self-Affine Tiling of Polyhedra
AbstractWe obtain a complete classification of polyhedral sets (unions of finitely many convex polyhedra) that admit self-affine tilings, i.e.,...
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Remarks on Analogies Between Haar Meager Sets and Haar Null Sets
In the paper some analogies between Haar meager sets and Haar null sets in abelian Polish groups are presented.
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Generic measure preserving transformations and the closed groups they generate
We show that, for a generic measure preserving transformation T , the closed group generated by T is not isomorphic to the topological group
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The structure of random homeomorphisms
In order to understand the structure of the “typical” element of a homeomorphism group, one has to study how large the conjugacy classes of the group...
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Nonsingular Poisson Suspensions
The classical Poisson functor associates to every infinite measure preserving dynamical system ( X, μ, T ) a probability preserving dynamical system ( X *...
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A Remark on Indicator Functions with Gaps in the Spectrum
Develo** a recent result of F . Nazarov and A . Olevskii, we show that for every subset a in ℝ of finite measure and every ε > 0 there exists b ⊂ ℝ...
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Mean equicontinuity, almost automorphy and regularity
The aim of this article is to obtain a better understanding and classification of strictly ergodic topological dynamical systems with (measurable)...