caa a22 4500 386360820 CHVBK 20180307111914.0 cr unu---uuuuu 161130e198904 xx s 000 0 eng 10.1017/S0004972700002677 doi S0004972700002677 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700002677 Rzezuchowski Tadeusz Institute of Mathematics, Warsaw Technical University, Pl.J.Robotniczej, 100-661 Warsaw, Poland Strong convergence of selections implied by weak [Elektronische Daten] [Tadeusz Rzezuchowski] In some situations weak convergence in L1, implies strong convergence. Let P, L: T → C(d) be measurable multifunctions (C(d) being the set of closed, convex subsets of d) the values L(t) affine sets and W(t) = P(t) L(t) extremal faces of P(t). Let pk be integrable selections of P, the projection of pk,(t) on L(t) and pk(t) on W(t). We prove that if converges weakly to zero then pk − k converges to zero in measure. We give also some extensions of this theorem. As applications to differential inclusions we investigate convergence of derivatives of convergent sequences of solutions and we describe solutions which are in some sense isolated. Finally we discuss what can be said about control functions u when the corresponding trajectories of ẋ = f(t, x, u) are convergent to some trajectory. Copyright © Australian Mathematical Society 1989 Bulletin of the Australian Mathematical Society Cambridge University Press 39/2(1989-04), 201-214 0004-9727 39:2<201 1989 39 BAZ https://doi.org/10.1017/S0004972700002677 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700002677 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rzezuchowski Tadeusz Institute of Mathematics, Warsaw Technical University, Pl.J.Robotniczej, 100-661 Warsaw, Poland NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 39/2(1989-04), 201-214 0004-9727 39:2<201 1989 39 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge