Let F: U subset of R-n --> R-m be a differentiable junction and p < m an integer. If k greater than or equal to 1 is an integer, alpha epsilon [0,1] and F epsilon Ck+(alpha), if we set C-p(F) = {x epsilon U / rank(Df(x)) less than or equal to p} then the Hausdorff measure of dimension (p + n-p/k+alpha) of F(C-p(F)) is zero.
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Inst Matematica Pura & Aplicada, BR-22460320 Rio De Janeiro, BrazilInst Matematica Pura & Aplicada, BR-22460320 Rio De Janeiro, Brazil
Moreira, Carlos Gustavo
Soares Ruas, Maria Aparecida
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Univ Sao Paulo, Dept Matemat, Inst Ciencias Matemat & Computacao, BR-13560970 Sao Carlos, SP, BrazilInst Matematica Pura & Aplicada, BR-22460320 Rio De Janeiro, Brazil
机构:
Univ Pau & Pays Adour, UMR CNRS 5142, Lab Math & Leurs Applicat, F-64013 Pau, FranceUniv Pau & Pays Adour, UMR CNRS 5142, Lab Math & Leurs Applicat, F-64013 Pau, France
Barbet, Luc
Dambrine, Marc
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Univ Pau & Pays Adour, UMR CNRS 5142, Lab Math & Leurs Applicat, F-64013 Pau, FranceUniv Pau & Pays Adour, UMR CNRS 5142, Lab Math & Leurs Applicat, F-64013 Pau, France
Dambrine, Marc
Daniilidis, Aris
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Univ Chile, Fac Ciencias, DIM CMM, Santiago, ChileUniv Pau & Pays Adour, UMR CNRS 5142, Lab Math & Leurs Applicat, F-64013 Pau, France