roposition
(LindebergFeller CLT). Let
is a family of r.v. such that
1.
,
2.
,
3.
.
Then for the following two conditions A,B to hold
A.
converges in distribution to
,
B.
is holospoudic (see the definition (
Holospoudic
))
it is necessary and sufficient that for each
we
have


(LindebergFeller condition)
