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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:
 5.8e+06 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
##### Keywords:
potential Fredholm functional; set of critical values
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##### References:
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