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The set of critical values of a potential Fredholm functional. (English. Russian original) Zbl 0922.58009
Math. Notes 63, No. 1, 118-120 (1998); translation from Mat. Zametki 63, No. 1, 133-135 (1998).
The author proves the following analog for the class of \({\mathcal C}^\infty\) functionals defined on nonreflexive Banach spaces of the well-known Kupka-Sard theorem: Let \(V\) be a \({\mathcal C}^\infty\) potential Fredholm functional defined on a separable real Banach space \(E\). Then the set of critical values of \(V\) has Lebesgue measure zero.
MSC:
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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