Given a point set 
in the 
-dimensional unit cube 
, the star discrepancy is defined as
 |
(1)
|
where the local discrepancy is defined as
 |
(2)
|
is the content
of 
,
and 
is the class of all 
-dimensional
subintervals 
of 
of the form
 |
(3)
|
with 
for 
.
Here, the term "star" refers to the fact that the 
-dimensional subintervals have a vertex at the origin.
