proposition: Lemma lower_semicontinuous_measurable {R : realType} (f : R -> \bar R) : lower_semicontinuous f -> measurable_fun setT f.
proof: Proof. move=> scif; apply: (measurability (ErealGenOInfty.measurableE R)). move=> /= _ [_ [a ->]] <-; apply: measurableI => //; apply: open_measurable. by rewrite preimage_itv_o_infty; move/lower_semicontinuousP : scif; exact. 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