473

until m = li at which time there is no further change. Therefore, p = r since otherwise,there would exist a discrepancy right away in going from m= 1 to m= 2. Now suppose thesequence {li} is not equal to the sequence, {ki}. Then lr−b ̸= kr−b for some b a nonnegativeinteger taken to be a small as possible. Say lr−b > kr−b. Then, letting m = kr−b,

r

∑i=1

rank(Jli (0)

m)= r

∑i=1

rank(Jki (0)

m)and in going to m+1 a discrepancy must occur because the sum on the right will contributeless to the decrease in rank than the sum on the left. ■