This paper extends the theory of the core, the uncovered set, and the related undominated set to a general set of alternatives and an arbitrary measure space of voters. We investigate the properties of social preferences generated by simple games, we extend results on generic emptiness of the core, we prove the general nonemptiness of the uncovered and undominated sets, and we prove the upper h...

We establish some basic lower semicontinuity properties for a class of weigthed metrics in BV. These Riemann-type metrics, uniformly equivalent to the L 1 distance, are deened in terms of the Glimm interaction potential. They are relevant in the study of nonlinear hyperbolic systems of conservation laws, being contractive w.r.t. the corresponding ow of solutions.

In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of Type-2 Theory of Effectivity. This gives rise to a natural representation of the set M(X) of Borel probability measures on X. We compare this representation to a canonically constructed representation which encodes a Borel pro...

We deal with a family of functionals depending on curvatures and we prove for them compactness and semicontinuity properties in the class of closed and bounded sets which satisfy a uniform exterior and interior sphere condition. We apply the results to state an existence theorem for the Nitzberg and Mumford problem under this additional constraint. Ref. S.I.S.S.A. 85/99/M (July 99)

For every finite nonnegative measure ft we introduce the Sobolev spaces W^'(Q,K) and we study the lower semicontinuity of functionals of the form where the integrand / is quasiconvex.

We establish a general weak* lower semicontinuity result in the space BD(Ω) of functions of bounded deformation for functionals of the form

We show that the limit f of a weakly convergent sequence of W 1,1 homeomorphisms fj with finite distortion has finite distortion as well, provided that it is a homeomorphism. Moreover, the lower semicontinuity of the distortions is deduced both in case of outer and inner distortion.

In this paper, we concern with SLLN for sums of independent random upper-semicontinuous fuzzy sets. We first give a generalization of SLLN for sums of independent and level-wise identically distributed random fuzzy sets, and establish a SLLN for sums of random fuzzy sets which is independent and compactly uniformly integrable in the strong sense. As a result, a SLLN for sums of independent and ...

In this paper we study a metric Hopf-Lax formula looking in particular at the Carnot-Carathéodory case. We generalize many properties of the classical euclidean Hopf-Lax formula and we use it in order to get existence results for Hamilton-Jacobi-Cauchy problems satisfying a suitable Hörmander condition.

A lower semicontinuity result is proved in the space of special functions of bounded deformation for a fracture energetic model ∫ Ju Ψ([u], νu)dH , [u] · νu ≥ 0 H − a. e. on Ju. A characterization of the energy density Ψ, which ensures lower semicontinuity, is also given.