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Merged
affeldt-aist merged 19 commits into from
Oct 23, 2023
Merged

Lebesgue Stieltjes measure #677

affeldt-aist merged 19 commits into from
Oct 23, 2023

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@affeldt-aist affeldt-aist commented Jun 9, 2022 •
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Motivation for this change

This is an attempt at generalizing lebesgue_mesure.v.
RFC, FYI @hoheinzollern @IshiguroYoshihiro
We have only replayed the first part so far and plan to work on proving more properties soon.
Co-authored-by: @t6s

Things done/to do
  • added corresponding entries in CHANGELOG_UNRELEASED.md
  • added corresponding documentation in the headers
Automatic note to reviewers

Read this Checklist and put a milestone if possible.

@affeldt-aist affeldt-aist changed the title Lebesgue stieltjes measure Lebesgue Stieltjes measure Jun 9, 2022
@affeldt-aist affeldt-aist force-pushed the lebesgue_stieltjes_measure branch from 95f619d to 957048a Compare June 9, 2022 16:01
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zstone1 commented Jun 24, 2022

I've just checked out the lemma statements (not the proofs), and it looks pretty neat. The existing hlength_measure canonical instance provides a reasonably nice interface for it. And Hahn_ext_measure. One thing that makes me particularly happy about this is I think I can use this to state "spectral theorem". But I'm not 100% sure if it's general enough. That's something I'll look into shortly. In the meanwhile, I have only one question about this work. You carry around the (ndf : {homo f : x y / (x <= y)%R}) (rcf : right_continuous f conditions a lot. Which is fine while writing the proofs, but I can imagine this generating a lot of annoying side conditions when using them. Is there a nice way to package that up? Would a canonical structure for this make sense? Perhaps it's too cumbersome.

CohenCyril
CohenCyril reviewed Jul 7, 2022
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@affeldt-aist affeldt-aist force-pushed the lebesgue_stieltjes_measure branch from 957048a to 9981b71 Compare July 10, 2022 22:59
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@affeldt-aist affeldt-aist marked this pull request as ready for review October 6, 2022 13:01
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zstone1 reviewed Oct 6, 2022
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A few nitpicks and questions. The only meaningful change to consider would be explicitly building the Sogenfrey Line (in realfun.v?) instead of the "right_continuous" predicate. It won't change the proofs much either way, so it's easy to deal with it later. Up to you.

@hoheinzollern hoheinzollern mentioned this pull request Oct 7, 2022
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@affeldt-aist affeldt-aist force-pushed the lebesgue_stieltjes_measure branch from 41f1a00 to 5d39745 Compare October 21, 2022 02:33
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affeldt-aist commented Jan 26, 2023
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@affeldt-aist affeldt-aist added this to the 0.6.2 milestone Feb 23, 2023
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@affeldt-aist affeldt-aist added the enhancement ✨ This issue/PR is about adding new features enhancing the library label Mar 15, 2023
@affeldt-aist affeldt-aist modified the milestones: 0.6.2, 0.6.3 Apr 10, 2023
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CohenCyril
CohenCyril reviewed Oct 16, 2023
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theories/lebesgue_stieltjes_measure.v Outdated
(* x and y are real numbers *)
(* R.-ocitv == display for ocitv_type R *)
(* R.-ocitv.-measurable == semiring of sets of open-closed intervals *)
(* hlength f A := f b - f a with the hull of the set of real *)
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This should not be called hlength anymore.

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@affeldt-aist affeldt-aist Oct 23, 2023 •
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This has been renamed to wlength for weight (W is sometimes used in the literature and this seems to correspond to the original idea by Stieltjes, though he may have been using H at the time in fact).
The lemmas have been reworked a bit so that
the user can get along only with lemmas about lebesgue_measure,
wlength does not appear in proof scripts except in the proof of outer regularity
that exhibits wlength on purpose as far as I can see @zstone1 .

IshiguroYoshihiro and others added 18 commits October 23, 2023 15:56
@affeldt-aist affeldt-aist force-pushed the lebesgue_stieltjes_measure branch from d5653a9 to 3915fa4 Compare October 23, 2023 07:18
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affeldt-aist commented Oct 23, 2023

Wouah, CI green, thanks @proux01

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proux01 commented Oct 23, 2023

For what?

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affeldt-aist commented Oct 23, 2023

For what?

For the constant care to the infrastructure!

@affeldt-aist affeldt-aist mentioned this pull request Oct 23, 2023
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@affeldt-aist affeldt-aist merged commit 204edd9 into master Oct 23, 2023
affeldt-aist added a commit to affeldt-aist/analysis that referenced this pull request Oct 30, 2023
@affeldt-aist @IshiguroYoshihiro @t6s
Lebesgue Stieltjes measure (math-comp#677)
3c24dbd 
* tentative definition of lebesgue stieltjes measure

* cumulative function with HB

* put lebesgue_measure proof in module

---------

Co-authored-by: IshiguroYoshihiro <[email protected]>
Co-authored-by: [email protected]
Co-authored-by: Takafumi Saikawa <[email protected]>
proux01 pushed a commit that referenced this pull request Oct 30, 2023
@affeldt-aist @IshiguroYoshihiro
@t6s @proux01
Lebesgue Stieltjes measure (#677)
98403cd 
* tentative definition of lebesgue stieltjes measure

* cumulative function with HB

* put lebesgue_measure proof in module

---------

Co-authored-by: IshiguroYoshihiro <[email protected]>
Co-authored-by: [email protected]
Co-authored-by: Takafumi Saikawa <[email protected]>
@proux01 proux01 deleted the lebesgue_stieltjes_measure branch April 10, 2025 14:24
@motikaku motikaku mentioned this pull request Apr 23, 2025
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