proposition: Lemma nnfun_muleindic_ge0 d (T : measurableType d) (R : realDomainType) (f : {nnfun T >-> R}) r z : 0 <= r%:E * (\1_(f @^-1` [set r]) z)%:E.
proof: Proof. apply: (@mulef_ge0 _ _ (fun r => (\1_(f @^-1` [set r]) z)%:E)). by rewrite lee_fin// indicE. by move=> r0; rewrite preimage_nnfun0// indic0. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrnum ssrint interval finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality fsbigop ) signed reals ereal topology normedtype sequences real_interval esum measure lebesgue_measure numfun