Hence, L may be written in terms of y integration as: 



, , •'i I ^ / n ' 



L = lim 



k=l c , y n ; — 



nk /n 



/F 



- y c2 r 



n ii/ nk / 



k=l y >e/n / c , 



' ^ ' nk 



ii"i ^ >" ^L I y^ ^nk^^^ ^^ ■ 



Let B be the uniform bound on {c , } . 



nk 



(a) Proof of the conclusion under hypothesis [a) above: for a>0, 

 and fixed n,a, and b, define G(a) as: 



G(a] = / y'^ay"e "■'dy = — ~r- / e x dx 



[a] = / y2ay"e" ^dy = -j^ / 

 a ba 



Clearly Gfa) is a monotone decreasing function of a and G(a)-K) as 



a -> CO . 



Hence, including both tails of g , (y) , 





dy 



k=l y> 



nkl 



k=l -|y|>£LJl^ k=l y^^"^" 



-nk' 



n 



< 2 y 32 g(^^ ._ 2b2 cfi^^l - 



"" k=i l'"'^! I'"i^l 



as n tends to infinity 



(b) Proof of the co 

 satisfies hypothesis (a) with C = A, n = 0, a = 1, and b = 1 



(b) Proof of the conclusion under hypothesis (b) above: g 1^ (y) 



97 



