Skip to content

lemma extracted from the sampling branch to help rebasing #1592

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
affeldt-aist merged 1 commit into from
Apr 28, 2025
Merged

lemma extracted from the sampling branch to help rebasing #1592

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
3 changes: 3 additions & 0 deletions CHANGELOG_UNRELEASED.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -23,6 +23,9 @@
+ lemmas `in_set1`, `inr_in_set_inr`, `inl_in_set_inr`, `mem_image`, `mem_range`, `image_f`
+ lemmas `inr_in_set_inl`, `inl_in_set_inl`

- in `lebesgue_integral_approximation.v`:
+ lemma `measurable_prod`

### Changed

- in `pi_irrational`:
Expand Down
15 changes: 13 additions & 2 deletions theories/lebesgue_integral_theory/lebesgue_integral_approximation.v
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -576,8 +576,8 @@ Section measurable_sum.
Context d (T : measurableType d) (R : realType).
Implicit Types (D : set T) (f g : T -> R).

Lemma measurable_sum D I s (h : I -> (T -> R)) :
(forall n, measurable_fun D (h n)) ->
Lemma measurable_sum D I s (h : I -> T -> R) :
(forall i, measurable_fun D (h i)) ->
measurable_fun D (fun x => \sum_(i <- s) h i x).
Proof.
move=> mh; apply/measurable_EFinP.
Expand All @@ -586,6 +586,17 @@ rewrite (_ : _ \o _ = (fun t => \sum_(i <- s) (h i t)%:E)); last first.
by apply/emeasurable_sum => i; exact/measurable_EFinP.
Qed.

Lemma measurable_prod D (I : eqType) (s : seq I) (h : I -> T -> R) :
(forall i, i \in s -> measurable_fun D (h i)) ->
measurable_fun D (fun x => \prod_(i <- s) h i x).
Proof.
elim: s => [mh|x y ih mh].
by under eq_fun do rewrite big_nil//=; exact: measurable_cst.
under eq_fun do rewrite big_cons//=; apply: measurable_funM => //.
- by apply: mh; rewrite mem_head.
- by apply: ih => n ny; apply: mh; rewrite inE orbC ny.
Qed.

End measurable_sum.

Section emeasurable_comparison.
Expand Down
Loading