Talagrand's proof of the sufficiency of existence of a majorizing measure for the sample boundedness of processes with bounded increments used a contraction from a certain ultrametric space. We give a short proof of existence of such an ultrametric using admissible sequences of nets.
Étant donné un problème des moments classique de Hamburger, supposé indéterminé, on montre qu’une mesure solution est -canonique (N. I. Akhiezer, Oliver and Boyd, Edinburgh, 1965, p. 115) si et seulement si l’adhérence de l’espace des polynômes est exactement de codimension dans l’espace de Hilbert . On déduit de là des résultats de perturbation de mesures -canoniques généralisant ceux de C. Berg et J.-P. R. Christensen (Ann. Inst. Fourier, 31-3 (1981), 99–114), établis pour le cas des...
The main purpose is the introduction of an integral which covers most of the recent integrals which use fuzzy measures instead of measures. Before we give our framework for a fuzzy integral we motivate and present in a first part structure- and representation theorems for generalized additions and generalized multiplications which are connected by a strong and a weak distributivity law, respectively.
Based on results of generalized additions and generalized multiplications, proven in Part I, we first show a structure theorem on two generalized additions which do not coincide. Then we prove structure and representation theorems for generalized multiplications which are connected by a strong and weak distributivity law, respectively. Finally – as a last preparation for the introduction of a framework for a fuzzy integral – we introduce generalized differences with respect to t-conorms (which are...
Based on the results of generalized additions, multiplications and differences proven in Part I and II of this paper a framework for a general integral is presented. Moreover it is shown that many results of the literature are contained as special cases in our results.