Abstract
Let ( X , ‖ ⋅ ‖ ) be a reflexive Banach space with Kadec–Klee norm. Let f : X → ( − ∞ , + ∞ ] be a function which is either Lipschitzian or is proper, bounded below, and lower semi-continuous. Then f is supported from below by residually many parabolas opening downward, that is, the infimal convolution of ‖ ⋅ ‖ 2 and f is attained at residually many points of X.
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