������֧����$[0,\infty)$�ľֲ���ָ���ֲ���һ��������Ե����ɵȼ�����,
�����ʵ����������ƹ㵽��ȫ�ռ�. �ڴ˻�����,
�õ��˶Գƻ��ֲ��ľֲ������ԵĽ��. ������������̺�Embrechts
��Goldie (1980)\ucite{1}��Geluk (2004)\ucite{2}�Ǿֲ�����Ӧ���,
���в���֤����\cite{2}��.

This paper obtains some equivelent conditions
for a type of convolution closure of local subexponential
distributions on $[0,\infty)$, which are also valid for
distributions on $(-\infty,\infty)$ under certain conditions. On the
basis of these results, the local asymptotics for the distribution
of symmetrization are given. The results above include the
corresponding, non-local results of Embrechts and Goldie
(1980)\ucite{1} and Geluk (2004)\ucite{2}. Some of our proofs are
more simple than those of Geluk (2004)\ucite{2}.