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By Marchenko V. M.

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Let £ > 0 and let t G [0,1] \ > ! By lower semicontinuity of / and pointwise convergence of u^ to vP^, there is iV^ G N such that Wu'^it) - vP^it)\\ < e and that fiu'^it)) > / ( ^ ^ ( O ) - e for all m > N^. 1) we have the estimate fix) > f{u^{t))-e +{('"",x-u^{t)) - K""(«)k - a""{t)[\\x - u°°{t)f + 2\\x - «°°(t)|i£ + e^] Applying the previous Komlos convergences in the last inequality gives 50 C. Castaing, P. Raynaud de Fitte, A. 9 and is an epigraph extension of the preceding ones. 2. Let N = N U {CXD} and let Mbe a separable Hilbert space.

Let (//^) be a net in 3^([0,1], £([0,1]), A; X) which stably converges to some /x G 3^([0,1], £([0,1]), A; X). 1) liminf / f{t,x)dfi^{x)dt> ^ J[0,l]xX f{t,x)dfit{x)dt. 2 contains obviously all Suslin metrizable spaces, in particular it contains all Polish spaces. Here is an example where X is not metrizable. 3 (tempered distributions). 4] and the references therein. The following example comes Variational convergence results with applications to evolution inclusions 39 from [21]: If E is a separable Frechet space, then the dual E* of E, endowed with the topology TC of uniform convergence on compact subsets of E, is a submetrizable A:^;-space.

We begin with the following evolution inclusion governed by a subdifferential operator with perturbation containing Young measures. 1. be a separable Hilbert space, and IK a compact set in H. Let us consider a Caratheodory integrand 7 defined on [0,1] x IHI x Y satisfying: 1) There exists (3 G L^+ ([0,1]) such that \-i[t,xi,y)--i[t,X2,y)\

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