proposition: Lemma subspace_continuous_measurable_fun (D : set R) (f : subspace D -> R) : measurable D -> continuous f -> measurable_fun D f.
proof: Proof. move=> mD /continuousP cf; apply: (measurability (RGenOpens.measurableE R)). move=> _ [_ [a [b ->] <-]]; apply: open_measurable_subspace => //. exact/cf/interval_open. Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum ssrint interval) mathcomp(finmap fingroup perm rat) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality fsbigop) reals ereal signed topology numfun normedtype HB(structures) sequences esum measure real_interval realfun exp lebesgue_stieltjes_measure