This paper provides a price equilibrium existence theorem in economies where commodities may be indivisible and aggregate excess demand functions may be discontinuous. We introduce a very weak notion of continuity, called recursive transfer lower semi-continuity, which is weaker than transfer lower semi-continuity and in turn weaker than lower semicontinuity. It is shown that the condition, tog...

We study nonlocal variational problems in Lp, like those that appear in peridynamics. The functional object of our study is given by a double integral. We establish characterizations of weak lower semicontinuity of the functional in terms of nonlocal versions of either a convexity notion of the integrand, or a Jensen inequality for Young measures. Existence results, obtained through the direct ...

This paper is concerned with upper semicontinuity of the family random attractors associated non-autonomous stochastic parabolic problems dominated by $ p $-Laplacian operator on thin domains in which domain collapses onto lower dimensional domain. The existence and uniqueness for equations are strictly proved an (n+1) $-dimensional domain, these established when n

In this note we give simplified proofs of rectifiability RCD(K,N) spaces as metric measure and lower semicontinuity the essential dimension, via \(\delta\)-splitting maps. The arguments are inspired by Cheeger-Colding theory for Ricci limits rely on second order differential calculus developed Gigli convergence stability results Ambrosio-Honda.

Epi-convergence in distribution is a useful tool in establishing limiting distributions of \argmin" estimators; however, it is not always easy to nd the epi-limit of a given sequence of objective functions. In this paper, we deene the notion of stochastic equi-lower-semicontinuity of a sequence of random objective functions. It is shown that epi-convergence in distribution and nite dimensional ...

Under new assumptions, we provide suffcient conditions for the upper and lower semicontinuity and continuity of the solution mappings to a class of generalized parametric set-valued Ky Fan inequality problems in linear metric space. These results extend and improve some known results in the literature e.g., Gong, 2008; Gong and Yoa, 2008; Chen and Gong, 2010; Li and Fang, 2010 . Some examples a...

We give an extension to a nonconvex setting of the classical radial representation result for lower semicontinuous envelope of a convex function on the boundary of its effective domain. We introduce the concept of radial uniform upper semicontinuity which plays the role of convexity, and allows to prove a radial representation result for nonconvex functions. An application to the relaxation of ...

We consider one type of stability (quasistability) of a vector combinatorial problem of finding the Pareto set. Under quasistability we understand a discrete analogue of lower semicontinuity by Hausdorff of the many-valued mapping, which defines the Pareto choice function. A vector problem on a system of subsets of a finite set (trajectorial problem) with non-linear partial criteria is in focus...