proposition: Lemma mu_ext0 : mu^* set0 = 0.
proof: Proof. apply/eqP; rewrite eq_le; apply/andP; split; last exact/mu_ext_ge0. rewrite /mu_ext; apply: ereal_inf_lb; exists (fun=> set0); first by split. by apply: lim_near_cst => //; near=> n => /=; rewrite big1. Unshelve. all: by end_near. 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)