proposition: Lemma fubini1a : (m1 \x m2).-integrable setT f <-> \int[m1]_x \int[m2]_y `|f (x, y)| < +oo.
proof: Proof. split=> [/integrableP[_]|] ioo; [|apply/integrableP; split=> [//|]]. - by rewrite -(fubini_tonelli1 (abse \o f))//=; exact: measurableT_comp. - by rewrite fubini_tonelli1//; exact: measurableT_comp. 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