proposition: Lemma ae_integrable1 : {ae m1, forall x, m2.-integrable setT (fun y => f (x, y))}.
proof: Proof. have : m1.-integrable setT (fun x => \int[m2]_y `|f (x, y)|). apply/integrableP; split => //. rewrite (le_lt_trans _ (fubini1a.1 imf))// ge0_le_integral //. - exact: measurableT_comp. - by move=> *; exact: integral_ge0. - by move=> *; rewrite gee0_abs//; exact: integral_ge0. move/integrable_ae => /(_ measurableT); apply: filterS => x /= /(_ I) im2f. apply/integrableP; split; first exact/measurableT_comp. by move/fin_numPlt : im2f => /andP[]. 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