proposition: Lemma content_ring_sup_sigma_additive (A : nat -> set T) : (forall i, measurable (A i)) -> measurable (\bigcup_i A i) -> trivIset [set: nat] A -> \sum_(i <oo) mu (A i) <= mu (\bigcup_i A i).
proof: Proof. move=> Am UAm At; rewrite lime_le//; first exact: is_cvg_nneseries. near=> n; rewrite big_mkord -measure_bigsetU//= le_measure ?inE//=. - exact: bigsetU_measurable. - by rewrite -bigcup_mkord; apply: bigcup_sub => i lein; apply: bigcup_sup. 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)