Some results on sets of positive measure in a metric space
Some Special Results of Convergent Sequences of Radon Measures.
Some theorems concerning the class of weight functions in the transformation theory for mesure space
Some theorems of Scorza-Dragoni type for multifunctions with application to the problem of existence of solutions for differential multivalued equations
Some theorems on measurable and continuous selections and some applications
Some thoughts about Segal's ergodic theorem
Over fifty years ago, Irving Segal proved a theorem which leads to a characterization of those orthogonal transformations on a Hilbert space which induce ergodic transformations. Because Segal did not present his result in a way which made it readily accessible to specialists in ergodic theory, it was difficult for them to appreciate what he had done. The purpose of this note is to state and prove Segal's result in a way which, I hope, will win it the recognition which it deserves.
Some topological properties of -covering sets
We prove the following theorems: There exists an -covering with the property . Under there exists such that is not an -covering or is not an -covering]. Also we characterize the property of being an -covering.
Some topologies on the set of lattice regular measures.
Some typical properties of dimensions of sets and measures.
Some uniformization results
Some versions of limit and Dieudonné-type theorems with respect to filter convergence for (ℓ)-group-valued measures
Some limit and Dieudonné-type theorems in the setting of (ℓ)-groups with respect to filter convergence are proved, extending earlier results.
Some Vitali theorems for Lebesgue Measure.
Sommes vectorielles d'ensembles de mesure nulle
Soit un groupe localement compact abélien ou un groupe de Lie et un compact parfait de . Il existe alors un compact de mesure de Haar nulle tel que soit d’intérieur non vide. En particulier si est métrisable, les seuls ensembles analytiques tels que soit de mesure nulle dès que l’est, sont dénombrables.
Sous-ensembles de courbes Ahlfors-régulières et nombres de Jones.
We prove that an Ahlfors-regular set (with dimension one) E ⊂ Rn which verifies a βq-version of P. W. Jones' geometric lemma is included in an Ahlfors-regular curve Γ.This theorem is due to G. David and S. Semmes, we give a more direct proof.
Sous-mesures symétriques sur un ensemble fini
Souvislost cyklické a radiální variace cesty s její délkou a ohybem
Spaces of generalized smoothness on h-sets and related Dirichlet forms
The paper is devoted to spaces of generalized smoothness on so-called h-sets. First we find quarkonial representations of isotropic spaces of generalized smoothness on ℝⁿ and on an h-set. Then we investigate representations of such spaces via differences, which are very helpful when we want to find an explicit representation of the domain of a Dirichlet form on h-sets. We prove that both representations are equivalent, and also find the domain of some time-changed Dirichlet form on an h-set.
Spaces of observables
Spaces of Test Functions and Theorems of the Bochner-Schoenberg-Eberlein Type.
Spaces of Vector-Valued Measurable Functions.