fact: Definition caratheodory_measurable (R : realType) (T : Type) (mu : set T -> \bar R) (A : set T) := forall X, mu X = mu (X `&` A) + mu (X `&` ~` A).
imports: mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality fsbigop ) reals ereal signed topology normedtype sequences esum numfun HB(structures)