This paper investigates the existence of pure strategy, dominant strategy, and mixed strategy Nash equilibria in discontinuous and/or nonconvex games. We introduce a new notion of very weak continuity, called weak transfer quasi-continuity, which is weaker than the most known weak notions of continuity, including diagonal transfer continuity in Baye et al. [1993] and better-reply security in Re...

The notion of continuity from above (upper continuity) for lattice-valued possibilistic measures as investigated in [7] has been proved to be a rather strong condition when imposed as demand on such a measure. Hence, our aim will be to introduce some versions of this upper continuity weakened in the sense that the conditions imposed in [7] to the whole definition domain of the possibilistic mea...

Abstract. Given a Calderón–Zygmund (C–Z for short) operator T , which satisfies Hörmander condition, we prove that: if T maps all the characteristic atoms to W L1, then T is continuous from Lp to Lp(1 < p < ∞). So the study of strong continuity on arbitrary function in Lp has been changed into the study of weak continuity on characteristic functions.

In this paper, some properties of the monotone set-valued function defined by the set-valued Choquet integral are discussed. It is shown that several important structural characteristics of the original set function, such as null-additivity, strong order continuity, property(S) and pseudometric generating property, etc., are preserved by the new set-valued function. It is also shown that integr...