Let 
be a discrete group. A unitary group representation 
on a Hilbert space 
has almost invariant vectors if, for
every finite subset 
and every 
,
there is a unit vector 
such that
 |
for every 
.
The group 
has Kazhdan's property (T) if every unitary representation of 
having almost invariant vectors has a nonzero invariant vector
,
meaning 
for every 
.
Equivalently, 
has a finite Kazhdan set 
and a constant 
for which the displayed condition forces the representation
to have a nonzero invariant vector.
