Schur-convexity of two types of one-parameter mean values in variables.
We define the notion of semicopula, a concept that has already appeared in the statistical literature and study the properties of semicopulas and the connexion of this notion with those of copula, quasi-copula, -norm.
We characterize some bivariate semicopulas and, among them, the semicopulas satisfying a Lipschitz condition. In particular, the characterization of harmonic semicopulas allows us to introduce a new concept of depedence between two random variables. The notion of multivariate semicopula is given and two applications in the theory of fuzzy measures and stochastic processes are given.
We continue our earlier investigations of radial subspaces of Besov and Lizorkin-Triebel spaces on . This time we study characterizations of these subspaces by differences.