Lebesgue Stieltjes measure #677

affeldt-aist · 2022-06-09T10:48:56Z

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.

zstone1 · 2022-06-24T23:12:36Z

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.

theories/lebesgue_stieltjes_measure.v

zstone1

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.

theories/lebesgue_stieltjes_measure.v

CohenCyril · 2023-10-16T15:37:16Z

theories/lebesgue_stieltjes_measure.v

+(*                          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        *)


This should not be called hlength anymore.

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 .

- up to sigma_sub_additive (wip)

- fix intermediate lemma - use continuity hypo

Co-authored-by: [email protected] Co-authored-by: Takafumi Saikawa <[email protected]>

affeldt-aist · 2023-10-23T10:31:25Z

Wouah, CI green, thanks @proux01

proux01 · 2023-10-23T10:36:31Z

For what?

affeldt-aist · 2023-10-23T10:39:43Z

For what?

For the constant care to the infrastructure!

* 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]>

affeldt-aist changed the title ~~Lebesgue stieltjes measure~~ Lebesgue Stieltjes measure Jun 9, 2022

affeldt-aist force-pushed the lebesgue_stieltjes_measure branch from 95f619d to 957048a Compare June 9, 2022 16:01

CohenCyril reviewed Jul 7, 2022

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affeldt-aist marked this pull request as ready for review October 6, 2022 13:01

zstone1 reviewed Oct 6, 2022

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hoheinzollern mentioned this pull request Oct 7, 2022

Lemma nondecreasing_right_continuousP now has e: {posnum R} #764

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IshiguroYoshihiro and others added 18 commits October 23, 2023 15:56

start lebesgue stieltjes measure

e3adffb

- up to sigma_sub_additive (wip)

tentative sketch for sigma_sub_additive

ab96f2d

progress wrt hlength_sigma_sub_additive

3f5cee0

- fix intermediate lemma - use continuity hypo

tentative definition of lebesgue stieltjes measure

9890a3c

cumulative function with HB

50cda6f

Co-authored-by: [email protected] Co-authored-by: Takafumi Saikawa <[email protected]>

upd and complete

97867e7

upd

35a1bfb

EFinf is actually er_map

11dc66f

use Content_SubSigmaAdditive_isMeasure.Build

3d7835e

rebase

41773f3

put lebesgue_measure proof in module

4614f3c

changelog, doc, minor fixes

886ee65

test

7f3ecfc

fix

ac085b4

fix

26f083f

rm dup, fix

84c0db8

fix

0358d24

rename hlength to wlength

3915fa4

affeldt-aist force-pushed the lebesgue_stieltjes_measure branch from d5653a9 to 3915fa4 Compare October 23, 2023 07:18

fix doc

d67d334

affeldt-aist mentioned this pull request Oct 23, 2023

introduce a file real_topology.v #1067

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affeldt-aist merged commit 204edd9 into master Oct 23, 2023
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Lebesgue Stieltjes measure #677

Lebesgue Stieltjes measure #677

affeldt-aist commented Jun 9, 2022 •

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zstone1 commented Jun 24, 2022

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CohenCyril Oct 16, 2023

affeldt-aist Oct 23, 2023 •

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affeldt-aist commented Oct 23, 2023

proux01 commented Oct 23, 2023

affeldt-aist commented Oct 23, 2023

Lebesgue Stieltjes measure #677

Lebesgue Stieltjes measure #677

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affeldt-aist commented Jun 9, 2022 • edited Loading

Motivation for this change

Things done/to do

Automatic note to reviewers

zstone1 commented Jun 24, 2022

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CohenCyril Oct 16, 2023

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affeldt-aist Oct 23, 2023 • edited Loading

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affeldt-aist commented Oct 23, 2023

proux01 commented Oct 23, 2023

affeldt-aist commented Oct 23, 2023

affeldt-aist commented Jun 9, 2022 •

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affeldt-aist Oct 23, 2023 •

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