The paper considers, for a given closed bounded set M ⊂ Rmand K = (0,1)n⊂ Rn, the set M = {h ϵ L2(K;Rm) | 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 hkϵ M(hk) there is h‘kϵ 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.
Raitums, U. (2009). On dependence of sets of functions on the mean value of their elements. Mathematical Modelling and Analysis, 14(1), 91-98. https://doi.org/10.3846/1392-6292.2009.14.91-98
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