We point out how capacities (non-additive measures) can be used to provide explanations about the concept of bivariate ageing function. The latter had been introduced to describe the family of the level sets of a survival function and motivated the interest toward the concept of semi-copula.

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...

5 PREFACE 7 LIST OF ORIGINAL PUBLICATIONS 8 RESEARCH INPUT AND AUTHORSHIP OF ARTICLES (I-IV) 9

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.