We show the sum of the first k Lyapunov exponents of linear cocycles is an upper semicontinuous function in the L topologies, for any 1 ≤ p ≤ ∞ and k. This fact, together with a result from Arnold and Cong, implies that the Lyapunov exponents of the L-generic cocycle, p < ∞, are all equal.

In this paper we prove that every proper convex and lower semicontinuous functional de ned on a real re exive Banach space X is semicoercive if and only if every small uniform perturbation of attains its minimum value on X.

We investigate two types of semicontinuity for set-valued maps, Painlevé–Kuratowski semicontinuity and Cesari’s property (Q). It is shown that, in the context of convexvalued maps, the concepts related to Cesari’s property (Q) have better properties than the concepts in the sense of Painlevé–Kuratowski. In particular, we give a characterization of Cesari’s property (Q) by means of upper semicon...

We show that if E is an equivalence of upper semicontinuous Fell bundles B and C over groupoids, then there is a linking bundle L(E ) over the linking groupoid L such that the full cross-sectional algebra of L(E ) contains those of B and C as complementary full corners, and likewise for reduced cross-sectional algebras. We show how our results generalise to groupoid crossed-products the fact, p...

We present some sufficient conditions ensuring the upper semicontinuity and the continuity of the Bregman projection operator ΠgC and the relative projection operator P g C in terms of the D-approximate (weak) compactness for a nonempty closed set C in a Banach space X. We next present certain sufficient conditions as well as equivalent conditions for the convexity of a Chebyshev subset of a Ba...

We study the local Lipschitz–continuity of the value function v associated with a Bolza Problem in presence of a Lagrangian L(x, q), convex and uniformly superlinear in q, but only Borel–measurable in x. Under these assumptions, the associated integral functional is not lower semicontinuous with respect to the suitable topology which assures the existence of minimizers, so all results known in ...

In the paper we study the continuity properties of the solution set of upper semicontinuous differential inclusions in both regularly and singularly perturbed case. Using a kind of dissipative type of conditions introduced in [1] we obtain lower semicontinuous dependence of the solution sets. Moreover new existence result for lower semicontinuous differential inclusions is proved.

This paper studies the generalized approximate set-valued equilibrium problems and furnishes some new existence results. The existence results for solutions are derived by using the celebrated KKM theorem and some concepts associated with the semi-continuity of the set-valued mappings such as outer-semicontinuity, inner-semicontinuity, upper-semicontinuity and so forth. The results achieved in ...

We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence. We also establish a sharp Harnack inequality for the minimal surface equation, which is crucial f...

Extrinsic and intrinsic characterizations are given for the class DSC(K) of differences of semi-continuous functions on a Polish space K, and also decomposition characterizations of DSC(K) and the class PS(K) of pointwise stabilizing functions on K are obtained in terms of behavior restricted to ambiguous sets. The main, extrinsic characterization is given in terms of behavior restricted to som...