The Motion of Disks in a Torus
The multifractal box dimensions of typical measures
We compute the typical (in the sense of Baire’s category theorem) multifractal box dimensions of measures on a compact subset of . Our results are new even in the context of box dimensions of measures.
The multifractal spectrum of discrete measures
The multifractal structure of super-brownian motion
The multiplier for the weak McShane integral
The multiplier for the weak McShane integral which has been introduced by M. Saadoune and R. Sayyad (2014) is characterized.
The multiplier-series of a Schottky group.
The Necessity of Strongly Subadditive Capacities for Neyman-Pearson Minimax Tests.
The Nikodym property and local properties of Boolean algebras
We study local interpolation properties and local supremum properties for a Boolean algebra. In particular, we present a new condition that is sufficient for the Nikodym property.
The Nikodym theorems for operator measures.
The one-sided ergodic Hilbert transform in Banach spaces
Let T be a power-bounded operator on a (real or complex) Banach space. We study the convergence of the one-sided ergodic Hilbert transform . We prove that weak and strong convergence are equivalent, and in a reflexive space also is equivalent to the convergence. We also show that (which converges on (I-T)X) is precisely the infinitesimal generator of the semigroup .
The Oppenheim series expansions and Hausdorff dimensions
The optional sampling theorem for convex set valued martingales.
The packing measure of the trajectory of a one-dimensional symmetric Cauchy process.
The Pascal adic transformation is loosely Bernoulli
The pathological infinity of measures
The Peano curves as limit of α-dense curves.
En este artículo presentamos una caracterización de las curvas de Peano como límite uniforme de sucesiones de curvas α-densas en el compacto que es llenado por la curva de Peano. Estas curvas α-densas deben tener densidades tendiendo a cero y sus funciones coordenadas deben de ser de variación tendiendo a infinito cuando α tiende a cero.
The Pełczyński property for some uniform algebras
The Perron product integral in Lie groups
The Poincaré Inequality Does Not Improve with Blow-Up
For each β > 1 we construct a family Fβ of metric measure spaces which is closed under the operation of taking weak-tangents (i.e. blow-ups), and such that each element of Fβ admits a (1, P)-Poincaré inequality if and only if P > β.
The point of continuity property, neighbourhood assignments and filter convergences
We show that for some large classes of topological spaces X and any metric space (Z,d), the point of continuity property of any function f: X → (Z,d) is equivalent to the following condition: (*) For every ε > 0, there is a neighbourhood assignment of X such that d(f(x),f(y)) < ε whenever . We also give various descriptions of the filters ℱ on the integers ℕ for which (*) is satisfied by the ℱ-limit of any sequence of continuous functions from a topological space into a metric space.