proposition: Lemma sigma_additive_is_additive (R : realFieldType) d (T : measurableType d) (mu : set T -> \bar R) : mu set0 = 0 -> sigma_additive mu -> additive mu.
proof: Proof. move=> mu0; rewrite -semi_sigma_additiveE -semi_additiveE. exact: semi_sigma_additive_is_additive. Qed.
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)