Skip to content

integrable and norm #1796

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

Open
affeldt-aist wants to merge 1 commit into
base: master
Choose a base branch
from
Open

integrable and norm #1796

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
5 changes: 4 additions & 1 deletion CHANGELOG_UNRELEASED.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -67,9 +67,12 @@
+ lemmas `measurable_giry_prod`, `giry_int_prod1`, `giry_int_prod2`

- in `measurable_realfun.v`:
+ lemmas `measurable_funN`
+ lemma `measurable_funN`
+ lemmas `nondecreasing_measurable`, `nonincreasing_measurable`

- in `lebesgue_integrable.v`:
+ lemma `integrable_norm`

### Changed

- in `charge.v`:
Expand Down
15 changes: 12 additions & 3 deletions theories/lebesgue_integral_theory/lebesgue_integrable.v
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -339,12 +339,21 @@ Qed.
End integrable_theory.
Arguments eq_integrable {d T R mu D} mD f.

Section measurable_bounded_integrable.
Section Rintegrable.
Context d {T : measurableType d} {R : realType}.
Variable mu : {measure set T -> \bar R}.
Implicit Types (D A B : set T) (f : T -> R).

Lemma measurable_bounded_integrable (f : T -> R) A (mA : measurable A) :
Lemma integrable_norm D f : mu.-integrable D (EFin \o f) ->
mu.-integrable D (EFin \o (normr \o f)).
Proof.
move=> /integrableP[mf foo]; apply/integrableP; split.
do 2 apply: measurableT_comp => //.
exact/measurable_EFinP.
by under eq_integral do rewrite /= normr_id.
Qed.

Lemma measurable_bounded_integrable f A (mA : measurable A) :
(mu A < +oo)%E -> measurable_fun A f ->
[bounded f x | x in A] -> mu.-integrable A (EFin \o f).
Proof.
Expand All @@ -355,7 +364,7 @@ have [M [_ mrt]] := bdA; apply: le_lt_trans.
by rewrite lte_mul_pinfty.
Qed.

End measurable_bounded_integrable.
End Rintegrable.

Lemma integrable_indic_itv {R : realType} (a b : R) (b0 b1 : bool) :
let mu := lebesgue_measure in
Expand Down