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Journal of Zhejiang University SCIENCE A

ISSN 1673-565X(Print), 1862-1775(Online), Monthly

2004 Vol.5 No.7 P.754-758

A general version of the Morse-Sard theorem

JIANG Hai-yi

Department of Mathematics, Zhejiang University, Hangzhou 310027, China

hyjiang@math.zju.edu.cn

Abstract: Let k, m, n be positive integers, and k≤2, α∈(0,1], 0k,α(Rm, Rn), A=Cr(f)={x∈Rm|rank(Df(x))≤r}, then f(A) is d-null. Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2.

Key words: Hausdorff measure, Rectifiable, Morse decomposition


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DOI:

10.1631/jzus.2004.0754

CLC number:

O174.12

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Received:

2003-09-30

Revision Accepted:

2004-01-08

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