Let 
be a set. Then a 
-algebra 
is a nonempty collection of subsets
of 
such that the following hold:
1. 
is in 
.
2. If 
is in 
,
then so is the complement of 
.
3. If 
is a sequence of elements of 
, then the union of the 
s is in 
.
If 
is any collection of subsets of 
, then we can always find a 
-algebra containing 
, namely the power set of 
. By taking the intersection
of all 
-algebras
containing 
,
we obtain the smallest such 
-algebra. We call the smallest 
-algebra containing 
the 
-algebra generated by 
.
