Random set functions
Random theorems in topology
Range of density measures
We investigate some properties of density measures – finitely additive measures on the set of natural numbers extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence as well as cluster points of some other similar sequences. We obtain range of possible values of density measures for any subset of . Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao [Bhaskara Rao, K. P. S., Bhaskara Rao,...
Rank and spectral multiplicity
For a dynamical system (X,T,μ), we investigate the connections between a metric invariant, the rank r(T), and a spectral invariant, the maximal multiplicity m(T). We build examples of systems for which the pair (m(T),r(T)) takes values (m,m) for any integer m ≥ 1 or (p-1, p) for any prime number p ≥ 3.
Rank is not a spectral invariant
Rank-one group actions with simple mixing -subactions.
Rate of convergence of conditional entropies for some maps of an interval
Ratio limit theorems and applications to ergodic theory
Rational Approximation and Weak Analyticity. I.
Rational Approximation and Weak Analyticity. II.
Real integrable spaces
Realcompactification and repleteness of Wallman spaces.
Realizing homomorphisms of category algebras
Rearrangement and convergence in spaces of measurable functions.
Recent progress on the Kakeya conjecture.
We survey recent developments on the Kakeya problem.[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].
Recherches sur les fonctions ayant une infinité d'oscillations et sur les fonctions discontinues
Recouvrements, derivation des mesures et dimensions.
Let X be a set with a symmetric kernel d (not necessarily a distance). The space (X,d) is said to have the weak (resp. strong) covering property of degree ≤ m [briefly prf(m) (resp. prF(m))], if, for each family B of closed balls of (X,d) with radii in a decreasing sequence (resp. with bounded radii), there is a subfamily, covering the center of each element of B, and of order ≤ m (resp. splitting into m disjoint families). Since Besicovitch, covering properties are known to be the main tool for...
Rectangle Exchange Transformations.
Rectifiability, analytic capacity, and singular integrals.
Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group
We construct an intrinsic regular surface in the first Heisenberg group equipped wiht its Carnot-Carathéodory metric which has euclidean Hausdorff dimension . Moreover we prove that each intrinsic regular surface in this setting is a -dimensional topological manifold admitting a -Hölder continuous parameterization.