Contribution à la mesure en analyse factorielle des données et applications

This thesis presents under a same cover a certain number of articles and studies that are regrouped into two parts. The first part, mostly theoretical, concerns some studies in the framework of factorial analysis. In the beginning several questions related to probability distribution functions appearing in factorial analysis are considereed, mainly about the evaluation and characterization of missing data. Then new results are given on projective transformations that allow to approach probability laws on compact sets. Finally another result on measureness (under the meaning of a given mass distribution) of two complementary subsets of convex sets defined by hyperplanes going through the gravity center. The second part aims at presenting a certain number of applications of Correspondence Factorial Analysis showing the diversity of concrete problems that can be invoked. It offers results of many studies conducted in France as in Lebanon in the framework of several researches that have facilitated the discovery of new information in very different sectors from experimental sciences going from earth science to economical, political and social sciences.