Continuous functions are dense in L1 #1015
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zstone1
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enhancement ✨
I have yet to use the lemma in a complete application to be sure but so far it looks ok. |
affeldt-aist
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Aug 29, 2023
CohenCyril
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Aug 30, 2023
IshiguroYoshihiro
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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 <[email protected]>
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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 <[email protected]>
proux01
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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 <[email protected]>
proux01
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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 <[email protected]>
proux01
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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 <[email protected]>
proux01
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TODO: MC2 port
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Motivation for this change
The last piece of track B for #965.
The proof starts with an integrable function
fgviaapproximation_sfun_integrablegis continuous.h.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
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 applyingcvg_ballPandfine_fcvgif that's easier for you.Things done/to do
CHANGELOG_UNRELEASED.mdCompatibility with MathComp 2.0
TODO: HB portto make sure someone ports this PR tothe
hierarchy-builderbranch or I already opened an issue or PR (please cross reference).Automatic note to reviewers
Read this Checklist and put a milestone if possible.