proposition: Lemma integrable_mkcond D f : measurable D -> mu.-integrable D f <-> mu.-integrable setT (f \_ D).
proof: Proof. move=> mD. rewrite unlock; apply: asbool_equiv; rewrite [in X in X <-> _]integral_mkcond. under [in X in X <-> _]eq_integral do rewrite restrict_abse. split => [|] [mf foo]. - by split; [exact/(measurable_restrict _ _ _ _).1| exact: le_lt_trans foo]. - by split; [exact/(measurable_restrict _ _ measurableT _).2| exact: le_lt_trans foo]. 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