Any distribution supported on 
with a mean differing
by say
from the nearest integer must belong to the set
of the previous section for 
. Thus
for large enough 
the set 
is a subset of
for some positive 
.
According to Theorem 1
for all 
in .
In view of the inequality
and 7 above we find
On the explosion set there is a 
(random) such that the right
hand of this
inequality is less than 
for all 
. A Taylor
expansion of the
logarithm thus shows
for all large 
and all in 
.
Since
almost surely the lemma is
proved.
