Let 



>0.r f > cos ^IES^zH . a .in ^JHHi^zll] 

 ^ I ml N m2 N / 



m^m^.i a{T^^^) y^;;^jm 



and 



^(N) ^ cnk Yn -* 



kf, = N 



Then , 



is in the form required for the application of the theorem in item 3. 



Since E[Y^ -^J = E[n ,,] = , condition (a) is satisfied. The 

 K a+K 



division by a(T('^)) satisfied condition (b) . The variance of xl^) 

 is given by: 



2 

 CNk 



But, 



a2 -^ Varfyf^M 



. r^ I ml I I m/ 1 



. a(T<«)yf;^ 



so. 



N var^"^^^^ ^ 



I ^^N = 4^I ^^k = Var(vf))B^ 

 k=l k=l 



which is bounded as N ->- o° . This verifies condition (d) 



100 



