Abstract
Sequential normal compactness is one of the most important properties in terms of modern variational analysis. It is necessary for the derivation of calculus rules for the computation of generalized normals to set intersections or preimages of sets under transformations. While sequential normal compactness is inherent in finite-dimensional Banach spaces, its presence has to be checked in the infinite-dimensional situation. In this paper, we show that broad classes of sets in Lebesgue and Sobolev spaces which are reasonable in the context of optimal control suffer from an intrinsic lack of sequential normal compactness.
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