yields SG ( y/λ ) as and CLDR holds with this S and α = (1 , 1 , 2). The next example demonstrates that the CLDR property may not hold for some G ( y ) even with q = p. Example 4.2. Consider with c = 0 . Then ¯ α = 2 . Consider an arbitrary 2 × 2 matrix S = ( s$_{ij}$ )$_{1}$$_{≤}$$_{i,j}$$_{≤}$$_{2}$ . Three possibilities could arise for ¯ α = 2 if CLDR were to hold so that ¯ a = α$_{1}$ + α$_{2}$. First, α$_{1}$ = α$_{2}$ = 1 , then does not exist, except if s$_{12}$ = s$_{22}$ = 0 , which is precluded for non-singular matrix S . G ( y ) =    y$_{1}$ 0 ( c + y$_{2}$ ) 2 y$_{1}$ ( c + y$_{2}$ )    lim λ →∞    λ 0 0 λ    SG ( y/λ )    2 y$_{1}$/λ 0 3 y 2 $_{3}$/λ 2 0 0 2 y$_{2}$/λ 0 3 y 2 $_{4}$/λ 2 0 0 3 y 2 $_{3}$/λ 2 3 y 2 $_{4}$/λ 2    19