In classical measure theory, the Radon-Nikodym theorem states in a concise condition, namely domination, how a measure can be factorized by another (bounded) measure through a density function. Several approaches have been undertaken to see under which conditions an exact factorization can be obtained with set functions that are not σ-additive (for instance finitely additive set functions or su...

In this paper we introduce four multigrid algorithms for the constrained minimization of non-quadratic functionals. The algorithm introduced in [L. Badea, Convergence rate of a Schwarz multilevel method for the constrained minimization of non-quadratic functionals, SIAM J. Numer. Anal., 44, 2, 2006, p. 449-477], has a sub-optimal computing complexity because the convex set, which is defined on ...

In this paper we deal with the set of k-additive belief functions dominating a given capacity. We follow the line introduced by Chateauneuf and Jaffray for dominating probabilities and continued by Grabisch for general k-additive measures. First, we show that the conditions for the general k-additive case lead to a very wide class of functions and this makes that the properties obtained for pro...

We prove that the convergence of a sequence of functions in the space L0 of measurable functions, with respect to the topology of convergence in measure, implies the convergence μ-almost everywhere (μ denotes the Lebesgue measure) of the sequence of rearrangements. We obtain nonexpansivity of rearrangement on the space L∞, and also on Orlicz spaces LN with respect to a finitely additive extende...

In this paper, we consider the dominance properties of the set of the pignistic k-additive belief functions. Then, given k, we conjecture the shape of the polytope of all the k-additive belief functions dominating a given belief function, starting from an analogy with the case of dominating probability measures. Under such conjecture, we compute the analytical form of the barycenter of the poly...

MOTIVATION Localizing protein binding sites within genomic DNA is of considerable importance, but remains difficult for protein families, such as transcription factors, which have loosely defined target sequences. It is generally assumed that protein affinity for DNA involves additive contributions from successive nucleotide pairs within the target sequence. This is not necessarily true, and no...

We study the least core, the kernel and bargaining sets of coalitional games with a countable set of players. We show that the least core of a continuous superadditive game with a countable set of players is a nonempty (norm-compact) subset of the space of all countably additive measures. Then we show that in such games the intersection of the prekernel and the least core is non-empty. Finally,...