Definition:Measurable Set/Also presented as

Measurable Set: Also presented as

Some sources present the Carathéodory condition as:

$\map {\mu^*} A = \map {\mu^*} {A \cap S} + \map {\mu^*} {A \cap \map \complement S}$

rather than using the $A \setminus S$ form.

While $A \cap \map \complement S$ is more unwieldy and cumbersome than $A \setminus S$, it does present the Carathéodory condition in a neatly symmetrical form.