Hausdorff measures and the Morse-Sard theorem.
Moreira, Carlos Gustavo T. de A.
Publicacions Matemàtiques, Tome 45 (2001), p. 149-162 / Harvested from Biblioteca Digital de Matemáticas
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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.

Publié le : 2001-01-01
DMLE-ID : 3941 
@article{urn:eudml:doc:41419,
     title = {Hausdorff measures and the Morse-Sard theorem.},
     journal = {Publicacions Matem\`atiques},
     volume = {45},
     year = {2001},
     pages = {149-162},
     mrnumber = {MR1829581},
     zbl = {0995.58007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41419}
}

Moreira, Carlos Gustavo T. de A. Hausdorff measures and the Morse-Sard theorem.. Publicacions Matemàtiques, Tome 45 (2001) pp. 149-162. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41419/