Boolean powers and stochastic spaces
Cardinalité, saturation et finitude
Completion of a class of topological semilattices, applications. (Complétion d'une classe de demi-treillis topologiques, applications.)
Continuous norms on locally convex spaces.
Correction to the paper: “Set-like equivalence and inner and outer cuts”
Coupures propres dans
Cyclic monads and their applications.
Cyclically compact operators in Banach spaces.
Definizione dei clan binari e loro classificazione
L’albero binario (libero) è una struttura analoga a quella dei numeri naturali (standard), salvo che ci sono due operazioni di successivo. Nello studio degli alberi binari non standard, si ha bisogno di strutture ordinate che stiano a quella di albero binario libero come la struttura (ordinata) Z sta ad N. Si introducono perciò i clan binari e se ne studiano le classi di isomorfismo. Si dimostra che esse sono determinate dalle classi di similitudine delle successioni numerabili di 2 elementi, avendo...
Der Hilbertsche Irreduzibilitätssatz.
Dimension of indiscernibility equivalences
Dimensional compactness in biequivalence vector spaces
The notion of dimensionally compact class in a biequivalence vector space is introduced. Similarly as the notion of compactness with respect to a -equivalence reflects our nonability to grasp any infinite set under sharp distinction of its elements, the notion of dimensional compactness is related to the fact that we are not able to measure out any infinite set of independent parameters. A fairly natural Galois connection between equivalences on an infinite set and classes of set functions ...
Endomorphic universes and their standard extensions
Enlargements of categories.
Existence d'un contrôle optimal via l'analyse non standard.
In this article, we want to show that it is possible to give a complete theory about the existence of an optimal control, without introducing any functional space, by means of the Non Standard Analysis.
Expected values in the alternative set theory and their applications to some limit theorems
This article presents an alternative approach to statistical moments within non-standard models and by the help of these moments some limit theorems are reformulated and proved.
Exploded and compressed numbers.
Exploded and compressed spaces.
Finitely-additive, countably-additive and internal probability measures
We discuss two ways to construct standard probability measures, called push-down measures, from internal probability measures. We show that the Wasserstein distance between an internal probability measure and its push-down measure is infinitesimal. As an application to standard probability theory, we show that every finitely-additive Borel probability measure on a separable metric space is a limit of a sequence of countably-additive Borel probability measures in the sense that for all bounded...
Fonctions Généralisées et Analyse Non Standard.