A Carathéodory extension of a premeasure 
on an algebra of sets 
over 
is a measure 
on the generated sigma-algebra 
that extends 
, so
 |
for every 
.
It is obtained by restricting the Carathéodory
measure induced by 
to 
.
The Carathéodory extension theorem guarantees that this extension exists. If 
is sigma-finite, then the extension is unique.
