proposition: Lemma EFin_measurable_fun d (T : measurableType d) (R : realType) (D : set T) (g : T -> R) : measurable_fun D (EFin \o g) <-> measurable_fun D g.
proof: Proof. split=> [mf mD A mA|]; last by move=> mg; exact: measurableT_comp. rewrite [X in measurable X](_ : _ = D `&` (EFin \o g) @^-1` (EFin @` A)). by apply: mf => //; exists A => //; exists set0; [constructor|rewrite setU0]. congr (_ `&` _);rewrite eqEsubset; split=> [|? []/= _ /[swap] -[->//]]. by move=> ? ?; exact: preimage_image. 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