Skip to content
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.

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

Refactoring lemmas about composition in Lebesgue Measure #925

Merged
merged 16 commits into from
May 15, 2023

Conversation

marcomole00
Copy link
Contributor

Motivation for this change

I've changed the formulation of some lemmas in the lebesgue measure theory.

The lemmas state that the measurability of functions in R is preserved when composed with

  • multiplication with a scalar
  • negation
  • exponentiation with a natural number
Things Done

Lemma measurable_funrM is now

Lemma measurable_funrM (D: set R) (k: R) : measurable_fun D ( *%R k).

instead of

Lemma measurable_funrM D f (k : R) : measurable_fun D f ->
measurable_fun D (fun x => k * f x).

Lemma measurable_funN is now

Lemma measurable_funN (D: set R) f : measurable_fun D (-%R ).

instead of

Lemma measurable_funN D f : measurable_fun D f -> measurable_fun D (-%R \o f).

Lemma measurable_fun_exprn is now

Lemma measurable_fun_exprn (D:set R) n : measurable_fun D ( (@GRing.exp R)^~ n) .

instead of

Lemma measurable_fun_exprn D n f :
measurable_fun D f -> measurable_fun D (fun x => f x ^+ n).

Lemma measurable_fun_sqr is now

Lemma measurable_fun_sqr (D: set R) f : measurable_fun D ( ( (@GRing.exp R)^~ 2%N)).

instead of

Lemma measurable_fun_sqr D f :

measurable_fun D f -> measurable_fun D (fun x => f x ^+ 2).
Automatic note to reviewers

Read this Checklist and put a milestone if possible.

@CohenCyril
Copy link
Member

I would name the non compositional lemmas operator_mesurable (e.g. mulr_measurable), and prove the other (former) lemmas from this using composition lemmas (unary and binary).

@affeldt-aist
Copy link
Member

Sorry, I failed to see you message before my nitpicking commit where I was essentially doing this renaming.

@affeldt-aist affeldt-aist self-requested a review May 13, 2023 13:14
Copy link
Member

@affeldt-aist affeldt-aist left a comment

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Thanks for your contribution Marco. You are surely right: the lemmas you pointed out ought better be provided in smaller lemmas to be composed with measurable_fun_comp. I just added a commit with a changelog and nitpicking. See CONTRIBUTING.md for a few clues about style.
Naming is not yet perfect but we'll have the occasion to come back to it when addressing #916.

- a few more hints for closing measurable_fun lemmas
- favoring composition leading to one lemma removal
- add deprecation for removed lemmas
@@ -1823,6 +1896,7 @@ move=> _ [_ [x ->] <-];rewrite esups_preimage setI_bigcupr.
by apply: bigcup_measurable => ? ?; exact/mf/emeasurable_itv.
Qed.

(*can this be changed?*)
Copy link
Member

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

This can indeed be changed advantageously by using measurable_fun_if provided lemmas about the measurability of boolean comparison operators (_ < _, etc.). This approach should trigger a bit of cleaning also and might better be done as a different PR.

@affeldt-aist affeldt-aist merged commit f30efd2 into math-comp:master May 15, 2023
@proux01 proux01 mentioned this pull request May 15, 2023
affeldt-aist added a commit that referenced this pull request May 15, 2023
favor use of `measurable_fun_comp`

Co-authored-by: Alessandro Bruni <[email protected]>
Co-authored-by: Reynald Affeldt <[email protected]>
Co-authored-by: affeldt-aist <[email protected]>
Co-authored-by: Pierre Roux <[email protected]>
IshiguroYoshihiro pushed a commit to IshiguroYoshihiro/analysis that referenced this pull request Sep 7, 2023
favor use of `measurable_fun_comp`

Co-authored-by: Alessandro Bruni <[email protected]>
Co-authored-by: Reynald Affeldt <[email protected]>
Co-authored-by: affeldt-aist <[email protected]>
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Labels
None yet
Projects
None yet
Development

Successfully merging this pull request may close these issues.

4 participants