Let 
be a sequence of analytic
functions regular in a region 
, and let this sequence be uniformly
convergent in every closed subset
of 
.
If the analytic function
 |
does not vanish identically, then if 
is a zero of 
of order 
, a neighborhood 
of 
and a number 
exist such that if 
, 
has exactly 
zeros in 
.
