150 RANDOM NUMBERS 3.5 First we know that
150 RANDOM NUMBERS 3.5 First we know that lim (~0, + ~1~ + . . . + Y(~-~)~) = i/bm, (16) n–too since the sequence is m-distributed. By Lemma E and Eq. (16), the theorem will be proved if we can show that lim sup (Y& + & + . . . + ytm-l),) I llmb2m-(17) n-03 This inequality is not obvious yet; some rather delicate maneuvering is necessary before we can prove it. Let q be a multiple of m, and consider qn) = c (44 -7 -q ). (18) Olj