Hausdorff measures and the Morse-Sard theorem.

Moreira, Carlos Gustavo T. de A.. "Hausdorff measures and the Morse-Sard theorem.." Publicacions Matemàtiques 45.1 (2001): 149-162. <http://eudml.org/doc/41419>.

@article{Moreira2001,
abstract = {Let F : U ⊂ Rn → Rm be a differentiable function and p &lt; 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.},
author = {Moreira, Carlos Gustavo T. de A.},
journal = {Publicacions Matemàtiques},
keywords = {Variedades diferenciables; Dimensión de Hausdorff; critical points; differentiable mappings; Hausdorff measure; Morse-Sard theorem},
language = {eng},
number = {1},
pages = {149-162},
title = {Hausdorff measures and the Morse-Sard theorem.},
url = {http://eudml.org/doc/41419},
volume = {45},
year = {2001},
}

TY - JOUR
AU - Moreira, Carlos Gustavo T. de A.
TI - Hausdorff measures and the Morse-Sard theorem.
JO - Publicacions Matemàtiques
PY - 2001
VL - 45
IS - 1
SP - 149
EP - 162
AB - Let F : U ⊂ Rn → Rm be a differentiable function and p &lt; 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.
LA - eng
KW - Variedades diferenciables; Dimensión de Hausdorff; critical points; differentiable mappings; Hausdorff measure; Morse-Sard theorem
UR - http://eudml.org/doc/41419
ER -