The product measure 
of the measure spaces 
and 
is the Carathéodory
extension of ![lambda:R->[0,infty]](/images/equations/ProductMeasure/Inline4.svg)
defined on the sigma-algebra of 
-measurable subsets of 
. Here 
is the collection of all measurable rectangles contained in 
, and 
is the premeasure defined
on 
by
 |
for 
,
where 
denotes the outer measure induced by the premeasure 
on 
.
