Let 
be a measure space and let 
be a measurable set with
. Let 
be a sequence of measurable
functions on 
such that each 
is finite almost everywhere in 
and 
converges almost everywhere
in 
to a finite limit. Then for every 
, there exists a subset 
of 
with 
such that 
converges uniformly on 
.
If 
and 
is either the class of Borel sets or the class of Lebesgue measurable sets, then the set 
can be chosen to be a closed
set.
