Hausdorff Measures and the Morse - Sard Theorem
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چکیده
Let F : U ⊂ Rn → Rm be a differentiable function and p < m an integer. If k ≥ 1 is an integer, α ∈ [0, 1] and F ∈ Ck+(α), if we set Cp(F ) = {x ∈ U | rank(Df(x)) ≤ p} then the Hausdorff measure of dimension (p + n−p k+α ) of F (Cp(F )) is zero.
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تاریخ انتشار 2001