Given a sequence of independent random variates 
, 
, ..., if 
and
 |
then
 |
This means that if the Lindeberg condition holds for the sequence of variates 
, ..., then the variance of
an individual term in the sum 
of 
is asymptotically negligible. For such sequences, the Lindeberg condition is necessary
as well as sufficient for the Lindeberg-Feller
central limit theorem to hold.
