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Continuous functions are dense in L1#1015

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zstone1 merged 8 commits intomath-comp:masterfrom
zstone1:continuous_l1
Aug 31, 2023
Merged

Continuous functions are dense in L1#1015
zstone1 merged 8 commits intomath-comp:masterfrom
zstone1:continuous_l1

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@zstone1 zstone1 commented Aug 27, 2023

Motivation for this change

The last piece of track B for #965.
The proof starts with an integrable function f

  1. Approximate that with a simple function g via approximation_sfun_integrable
  2. Use lusin's to get a compact region on which g is continuous.
  3. Use tietzes (and simple -> bounded) to extend g over to a continuous approximation, h.
  4. Chain these approximations together.

The proof could be factored out into more reusable components. However, having the topology for L1 is pretty important to make that work. Then we can circumvent most of the the boiler plate with

  • A filter convergences in a metric spaces <-> a corresponding sequence converges
  • Dense is transitive
    But without the Lp spaces defined, there's no great way to do this. I'm happy with things as they are now, mostly because I want to keep pushing towards FTC.

@affeldt-aist Is this phrasing of density ok? It's pretty easy to convert to one about (forall eps, exists N, ...) by applying cvg_ballP and fine_fcvg if that's easier for you.

Things done/to do
  • added corresponding entries in CHANGELOG_UNRELEASED.md
  • added corresponding documentation in the headers
Compatibility with MathComp 2.0
  • I added the label TODO: HB port to make sure someone ports this PR to
    the hierarchy-builder branch or I already opened an issue or PR (please cross reference).
Automatic note to reviewers

Read this Checklist and put a milestone if possible.

@zstone1 zstone1 added enhancement ✨ This issue/PR is about adding new features enhancing the library TODO: MC2 port This PR must be ported to mathcomp 2 now that the. Remove this label when the port is done. labels Aug 27, 2023
@zstone1 zstone1 requested a review from affeldt-aist August 27, 2023 20:19
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@affeldt-aist Is this phrasing of density ok?

I have yet to use the lemma in a complete application to be sure but so far it looks ok.

@zstone1 zstone1 merged commit 2a479b4 into math-comp:master Aug 31, 2023
IshiguroYoshihiro pushed a commit to IshiguroYoshihiro/analysis that referenced this pull request Sep 7, 2023
* simple functions are bounded

* continuous functions dense in simple

* updating changelog

* proving full theorem instead

* changelog

* shorter simple_bouned with bigmax lemmas

* fix, mv 1 lemma, marginally shorter scripts

* making lemma non-local

---------

Co-authored-by: Reynald Affeldt <reynald.affeldt@aist.go.jp>
affeldt-aist added a commit to affeldt-aist/analysis that referenced this pull request Sep 21, 2023
* simple functions are bounded

* continuous functions dense in simple

* updating changelog

* proving full theorem instead

* changelog

* shorter simple_bouned with bigmax lemmas

* fix, mv 1 lemma, marginally shorter scripts

* making lemma non-local

---------

Co-authored-by: Reynald Affeldt <reynald.affeldt@aist.go.jp>
proux01 pushed a commit that referenced this pull request Sep 22, 2023
* simple functions are bounded

* continuous functions dense in simple

* updating changelog

* proving full theorem instead

* changelog

* shorter simple_bouned with bigmax lemmas

* fix, mv 1 lemma, marginally shorter scripts

* making lemma non-local

---------

Co-authored-by: Reynald Affeldt <reynald.affeldt@aist.go.jp>
proux01 pushed a commit that referenced this pull request Sep 25, 2023
* simple functions are bounded

* continuous functions dense in simple

* updating changelog

* proving full theorem instead

* changelog

* shorter simple_bouned with bigmax lemmas

* fix, mv 1 lemma, marginally shorter scripts

* making lemma non-local

---------

Co-authored-by: Reynald Affeldt <reynald.affeldt@aist.go.jp>
proux01 pushed a commit that referenced this pull request Sep 25, 2023
* simple functions are bounded

* continuous functions dense in simple

* updating changelog

* proving full theorem instead

* changelog

* shorter simple_bouned with bigmax lemmas

* fix, mv 1 lemma, marginally shorter scripts

* making lemma non-local

---------

Co-authored-by: Reynald Affeldt <reynald.affeldt@aist.go.jp>
@proux01 proux01 removed the TODO: MC2 port This PR must be ported to mathcomp 2 now that the. Remove this label when the port is done. label Sep 25, 2023
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4 participants