On the Cohomology of a Hyperfine Action.
On the completeness of -spaces over a charge
On the complexification of the Weierstrass non-differentiable function.
On the complexity of some -ideals of -P-porous sets
Let be a porosity-like relation on a separable locally compact metric space . We show that the -ideal of compact --porous subsets of (under some general conditions on and ) forms a -complete set in the hyperspace of all compact subsets of , in particular it is coanalytic and non-Borel. Our general results are applicable to most interesting types of porosity. It is shown in the cases of the -ideals of -porous sets, --porous sets, -strongly porous sets, -symmetrically porous sets...
On the complexity of sums of Dirichlet measures
Let be the set of all Dirichlet measures on the unit circle. We prove that is a non Borel analytic set for the weak* topology and that is not norm-closed. More precisely, we prove that there is no weak* Borel set which separates from (or even , the set of all measures singular with respect to every measure in . This extends results of Kaufman, Kechris and Lyons about and and gives many examples of non Borel analytic sets.
On the conditional expectation in a regular ordered space
On the conformal gauge of a compact metric space
In this article we study the Ahlfors regular conformal gauge of a compact metric space , and its conformal dimension . Using a sequence of finite coverings of , we construct distances in its Ahlfors regular conformal gauge of controlled Hausdorff dimension. We obtain in this way a combinatorial description, up to bi-Lipschitz homeomorphisms, of all the metrics in the gauge. We show how to compute using the critical exponent associated to the combinatorial modulus.
On the Connectedness of Ergodic Systems.
On the connection between Hausdorff measures and generalized capacity
On the construction of outer measures with values in a uniform semigroup
On the continuity of certain non-additive set functions
On the continuity of the Faber mapping
On the continuity of the semivariation in locally convex spaces
On the control measures of vector measures.
Si Σ es una σ-álgebra y X un espacio localmente convexo se estudian las condiciones para las cuales una medida vectorial σ-aditiva γ : Σ → χ tenga una medida de control μ. Si Σ es la σ-álgebra de Borel de un espacio métrico, se obtienen condiciones necesarias y suficientes usando la τ aditividad de γ. También se dan estos resultados para las polimedidas.
On the correct discrimination of Gaussian hypotheses. II.
On the countable generator theorem
Let T be a finite entropy, aperiodic automorphism of a nonatomic probability space. We give an elementary proof of the existence of a finite entropy, countable generating partition for T.
On the covering by small random intervals
On the decomposition of continuous flows on the Polish space
On the density maxima of a function
On the derivation and covering properties of a differentiation basis