diff --git a/CHANGELOG_UNRELEASED.md b/CHANGELOG_UNRELEASED.md index 05d044edfa..b5f05e6a97 100644 --- a/CHANGELOG_UNRELEASED.md +++ b/CHANGELOG_UNRELEASED.md @@ -96,6 +96,8 @@ - in `hoelder.v`: + lemmas `Lnorm_abse`, `Lfun_norm` +- in `lebesgue_integral_fubini.v`: + + lemmas `integral21_prod_meas2`, `integral12_prod_meas2` ### Changed @@ -236,6 +238,10 @@ - in `hoelder.v`: + `minkowski` -> `minkowski_EFin` +- in `lebesgue_integral_fubiniv.`: + + `fubini1` -> `integral12_prod_meas1` + + `fubini2` -> `integral21_prod_meas1` + ### Generalized - in `derive.v`: diff --git a/theories/lebesgue_integral_theory/lebesgue_integral_fubini.v b/theories/lebesgue_integral_theory/lebesgue_integral_fubini.v index 8be92cff29..472e68f8cf 100644 --- a/theories/lebesgue_integral_theory/lebesgue_integral_fubini.v +++ b/theories/lebesgue_integral_theory/lebesgue_integral_fubini.v @@ -964,29 +964,45 @@ apply: ge0_le_integral; [by []|by []|exact: measurableT_comp|..]. + by move=> x _; rewrite gee0_abs// -/((abse \o f) (x, y)) fune_abse leeDr. Qed. -Lemma fubini1 : \int[m1]_x F x = \int[m1 \x m2]_z f z. +Lemma integral12_prod_meas1 : \int[m1]_x F x = \int[m1 \x m2]_z f z. Proof. rewrite FE integralB; [|by[]|exact: integrable_Fplus|exact: integrable_Fminus]. by rewrite [in RHS]integralE ?fubini_tonelli1//; [exact: measurable_funeneg|exact: measurable_funepos]. Qed. -Lemma fubini2 : \int[m2]_x G x = \int[m1 \x m2]_z f z. +Lemma integral21_prod_meas1 : \int[m2]_x G x = \int[m1 \x m2]_z f z. Proof. rewrite GE integralB; [|by[]|exact: integrable_Gplus|exact: integrable_Gminus]. by rewrite [in RHS]integralE ?fubini_tonelli2//; [exact: measurable_funeneg|exact: measurable_funepos]. Qed. +Lemma integral21_prod_meas2 : \int[m2]_x G x = \int[m1 \x^ m2]_z f z. +Proof. +rewrite integral21_prod_meas1; apply: eq_measure_integral => //= A mA _. +by apply: product_measure_unique => // B C mB mC/=; rewrite product_measure2E. +Qed. + +Lemma integral12_prod_meas2 : \int[m1]_x F x = \int[m1 \x^ m2]_z f z. +Proof. +rewrite integral12_prod_meas1//; apply: eq_measure_integral => //= A mA _. +by apply: product_measure_unique => // B C mB mC/=; rewrite product_measure2E. +Qed. + Theorem Fubini : \int[m1]_x \int[m2]_y f (x, y) = \int[m2]_y \int[m1]_x f (x, y). -Proof. by rewrite fubini1 -fubini2. Qed. +Proof. by rewrite integral12_prod_meas1 -integral21_prod_meas1. Qed. End fubini. #[deprecated(since="mathcomp-analysis 1.10.0", note="renamed to `integrable12ltyP`")] Notation fubini1a := integrable12ltyP (only parsing). #[deprecated(since="mathcomp-analysis 1.10.0", note="renamed to `integrable21ltyP`")] Notation fubini1b := integrable21ltyP (only parsing). +#[deprecated(since="mathcomp-analysis 1.12.0", note="renamed to `integral12_prod_meas1`")] +Notation fubini1 := integral12_prod_meas1 (only parsing). +#[deprecated(since="mathcomp-analysis 1.12.0", note="renamed to `integral21_prod_meas1`")] +Notation fubini2 := integral21_prod_meas1 (only parsing). Section sfinite_fubini. Local Open Scope ereal_scope.