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Let (X1,X2,…,Xn) and (Y1,Y2,…,Yn) be real random vectors with the same ∑n i=1 Xi≤cx ∑n i=1 Yi and max1≤k≤n ∑k i=1 Xi≤icx max1≤k≤n ∑k i=1Yi hold. Based on this fact, a more general comparison theorem is obtained.