Mesures vectorielles et partitions continues de l'unité
Metric diophantine approximation in Julia sets of expanding rational maps
Metric Diophantine approximation on the middle-third Cantor set
Let be a real number and let denote the set of real numbers approximable at order at least by rational numbers. More than eighty years ago, Jarník and, independently, Besicovitch established that the Hausdorff dimension of is equal to . We investigate the size of the intersection of with Ahlfors regular compact subsets of the interval . In particular, we propose a conjecture for the exact value of the dimension of intersected with the middle-third Cantor set and give several results...
Metric properties of alternating Lüroth series
Metric properties of positively ordered monoids.
Metric properties of some planar sets
Metric spaces admitting only trivial weak contractions
If (X,d) is a metric space then a map f: X → X is defined to be a weak contraction if d(f(x),f(y)) < d(x,y) for all x,y ∈ X, x ≠ y. We determine the simplest non-closed sets X ⊆ ℝⁿ in the sense of descriptive set-theoretic complexity such that every weak contraction f: X → X is constant. In order to do so, we prove that there exists a non-closed set F ⊆ ℝ such that every weak contraction f: F → F is constant. Similarly, there exists a non-closed set G ⊆ ℝ such that every weak contraction...
Metrics on vector spaces with -localisation.
Micro tangent sets of continuous functions
Motivated by the concept of tangent measures and by H. Fürstenberg’s definition of microsets of a compact set we introduce micro tangent sets and central micro tangent sets of continuous functions. It turns out that the typical continuous function has a rich (universal) micro tangent set structure at many points. The Brownian motion, on the other hand, with probability one does not have graph like, or central graph like micro tangent sets at all. Finally we show that at almost all points Takagi’s...
Midpoint convex functions majorized by midpoint concave functions.
Midpoint convex functions majorized by midpoint concave functions. (Short Communication).
Miery v kartézských súčinoch
Mild law of large numbers and its consequences
Minimal complementation and maximal conjugation for partitions, with an application to Blackwell sets
Minimal generators for aperiodic endomorphisms
Every aperiodic endomorphism of a nonatomic Lebesgue space which possesses a finite 1-sided generator has a 1-sided generator such that . This is the best estimate for the minimal cardinality of a 1-sided generator. The above result is the generalization of the analogous one for ergodic case.
Minimal generators for ergodic endomorphisms
Minimal models for -actions
We prove that on a metrizable, compact, zero-dimensional space every -action with no periodic points is measurably isomorphic to a minimal -action with the same, i.e. affinely homeomorphic, simplex of measures.
Minimal paradoxical decomposition for Mycielski's square
Minimal Self-Joinings and Positive Topological Entropy.
Minimal self-joinings and positive topological entropy II
An effective construction of positive-entropy almost one-to-one topological extensions of the Chacón flow is given. These extensions have the property of almost minimal power joinings. For each possible value of entropy there are uncountably many pairwise non-conjugate such extensions.