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Let k, m, n be positive integers, and k≥2, a∈(0,1], 0＜r＜min{m,n} an integer, d=r+(m-r)/(k+a), and if f∈C^k,a(IR^m,IR^n),A=Cr(f)={x∈IR^m|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.