We introduce the concept of fuzzy co-r-M -semicontinuous, and investigate the relationships between fuzzy co-r-M -semicontinuous mappings and several types of fuzzy r-minimal semicompactness.

The existence of a Richter–Peleg multi-utility representation of a preorder by means of upper semicontinuous or continuous functions is discussed in connection with the existence of a Richter–Peleg utility representation. We give several applications that include the analysis of countable Richter–Pelegmulti-utility representations.

Abstract: We provide a new proof of the upper-semicontinuity property for the global attractors admitted by the solution operators associated with some strongly damped wave equations. In particular, we demonstrate an explicit control over semidistances between trajectories in the weak energy phase space in terms of the perturbation parameter. This result strengthens the recent work by Y. Wang a...

A general lower semicontinuity theorem, in which not only mappings uM and PM but also the integrands fM depend on M , is proved for integrands f, fM under certain general hypotheses including that f(x, u, P ) is convex respect to P and fM converge to f locally uniformly, but fM (x, u, P ) are not required to be convex respect to P and fM (x, ·, ·) do not even need to be lower semicontinuous. So...

We obtain necessary and sufficient conditions in the Large Deviation Principle for random upper semicontinuous functions on a separable Banach space. The main tool is the recent work of Arcones on the LDP for empirical processes.

Based on some ideas of Greene and Krantz, we study the semicontinuity of automorphism groups of domains in one and several complex variables. We show that semicontinuity fails for domains in C, n > 1, with Lipschitz boundary, but it holds for domains in C1 with Lipschitz boundary. Using the same ideas, we develop some other concepts related to mappings of Lipschitz domains. These include Bergma...

We extend some topologies on the space of upper semicontinuous functions with compact support to those on that of general upper semicontinuous functions and see that graphical topology and modified L topology are the same. We then define random upper semicontinuous functions using their topological Borel field and finally give a Choquet theorem for random upper semicontinuous functions.