For sigma-finite measure spaces 
and 
, the product measure 
is the unique measure
on the product sigma-algebra 
satisfying
 |
for every measurable rectangle 
with 
and 
, using the convention 
. The measurable rectangles form a semiring
that generates 
;
the rectangle formula defines a premeasure there,
and its Carathéodory extension is
the product measure.
