This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Henrion, RenéSeeger, Alberto2016-03-242019-06-2820080946-8633https://doi.org/10.34657/3456https://oa.tib.eu/renate/handle/123456789/1965The lower limit of a sequence of closed convex processes is again a closed convex process. In this note we prove the following uniform boundedness principle: if the lower limit is nonempty-valued everywhere, then, starting from a certain index, the given sequence is uniformly norm-bounded. As shown with an example, the uniform boundedness principle is not true if one drops convexity. By way of illustration, we consider an application to the controllability analysis of differential inclusions.application/pdfeng510Convex processespositively homogeneous mapscontrollabilityPainlev´e-Kuratowski limitsgraph-convergenceReport