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CLC number: O174.12

On-line Access: 2024-08-27

Received: 2023-10-17

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Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.7 P.754-758

http://doi.org/10.1631/jzus.2004.0754


A general version of the Morse-Sard theorem


Author(s):  JIANG Hai-yi

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   hyjiang@math.zju.edu.cn

Key Words:  Hausdorff measure, Rectifiable, Morse decomposition


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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.

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