Proofs of Results of Chapter I

Abstract

It is convenient in all the proofs to normalize the weights ${W_n}: = \left\{ {{W_{{i,n}}}\;,\;1 \leqslant i \leqslant n} \right\}$ in defining

$$ W_i^{{(n)}}\;: = n{W_{{i,n}}}\,,\;1 \leqslant i \leqslant n\;, $$

which ensures that W_i ⁽ⁿ⁾. is of the order of δ_W,n. in probability. We also abridge S(P) in S.