Contre-exemples associés aux théorèmes de Rosenthal. Quelques propriétés liées à ces résultats
Convergence almost everywhere of sequences of measurable functions
Convergence diffuse d'une suite de fonctions
Convergence of conditional expectations
Convergence of sequences of real functions with respect to small systems
Convergence theorems for a Daniell-Loomis integral.
Convergence theorems for the PU-integral
We give a definition of uniform PU-integrability for a sequence of -measurable real functions defined on an abstract metric space and prove that it is not equivalent to the uniform -integrability.
Correction to “On the non-measurability of a certain mapping”
Deux exemples de fonctions non mesurables
Die Cantorsche Abbildung ist ein Borel-Isomorphismus.
Difference functions of periodic measurable functions
We investigate some problems of the following type: For which sets H is it true that if f is in a given class ℱ of periodic functions and the difference functions are in a given smaller class G for every h ∈ H then f itself must be in G? Denoting the class of counter-example sets by ℌ(ℱ,G), that is, , we try to characterize ℌ(ℱ,G) for some interesting classes of functions ℱ ⊃ G. We study classes of measurable functions on the circle group that are invariant for changes on null-sets (e.g. measurable...
DiPerna-Majda measures and uniform integrability
The purpose of this note is to discuss the relationship among Rosenthal's modulus of uniform integrability, Young measures and DiPerna-Majda measures. In particular, we give an explicit characterization of this modulus and state a criterion of the uniform integrability in terms of these measures. Further, we show applications to Fatou's lemma.
Dynamics via measurability.
Egoroff, σ, and convergence properties in some archimedean vector lattices
An archimedean vector lattice A might have the following properties: (1) the sigma property (σ): For each there are and a ∈ A with λₙaₙ ≤ a for each n; (2) order convergence and relative uniform convergence are equivalent, denoted (OC ⇒ RUC): if aₙ ↓ 0 then aₙ → 0 r.u. The conjunction of these two is called strongly Egoroff. We consider vector lattices of the form D(X) (all extended real continuous functions on the compact space X) showing that (σ) and (OC ⇒ RUC) are equivalent, and equivalent...
El espacio de la convergencia en medida y su dual.
El teorema de convergencia de Vitali sobre integración término a término.
Entropy on effect algebras with Riesz decomposition property II: MV-algebras
We study the entropy mainly on special effect algebras with (RDP), namely on tribes of fuzzy sets and sigma-complete MV-algebras. We generalize results from [RiMu] and [RiNe] which were known only for special tribes.
Entropy on effect algebras with the Riesz decomposition property I: Basic properties
We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.
Equilibrium points of random generalized games.
Estimating mathematical information on Graphs: A Scientific Approach