Skip to content

add variant of Fubini lemmas and rename to clarify #1651

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
proux01 merged 1 commit into from
Jul 1, 2025
+25 −3
Merged

add variant of Fubini lemmas and rename to clarify #1651

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
6 changes: 6 additions & 0 deletions CHANGELOG_UNRELEASED.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -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

Expand Down Expand Up @@ -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`:
Expand Down
22 changes: 19 additions & 3 deletions theories/lebesgue_integral_theory/lebesgue_integral_fubini.v
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -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.
Expand Down
Loading