On dependence of sets of functions on the mean value of their elements - Raitums, Uldis (Mathematical Modelling and Analysis, 2009)
The paper considers, for a given closed bounded set M ⊂ R m and K = (0,1) n ⊂ R n , the set M = h ϵ L2 (K;R m ) | h(x) ϵ M a.e.x ϵ K and its subsets It is shown that, if a sequence hk ⊂ coM converges to an element hk ϵ M(hk ) there is h‘k ϵ M(ho ) such that h’k - hk → 0 as k → ∞ . If, in addition, the set M is finite or M is the convex hull of a finite set of elements, then the multivalued mapping h → M(h) is lower semicontinuous on coM. First published online: 14 Oct 2010