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[Merged by Bors] - feat: Rademacher theorem#7003

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sgouezel wants to merge 133 commits intomasterfrom
rademacher
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[Merged by Bors] - feat: Rademacher theorem#7003
sgouezel wants to merge 133 commits intomasterfrom
rademacher

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@sgouezel sgouezel commented Sep 7, 2023

kodyvajjha pushed a commit that referenced this pull request Sep 22, 2023
First calculus prerequisites for Rademacher theorem in #7003.

Add a few lemmas that were available for `FDeriv` but not for `Deriv`, weaken assumptions here and there.
kodyvajjha pushed a commit that referenced this pull request Sep 22, 2023
Prerequisite for Rademacher's theorem in #7003

We currently have in mathlib the Fréchet derivative, and the derivative of maps defined on the scalar field. In this PR, we introduce another notion, the derivative along a line. It is more elementary (but less well behaved) than the full Fréchet derivative.

The API is essentially copied from the file on the one-dimensional derivative, with a few additions that have proved useful for Rademacher's theorem. The API could definitely be expanded, but it's already heavy... I have put everything in the single file `LineDeriv/Basic.lean`, mimicking the directory structure for `FDeriv` and `Deriv` and leaving open the possibility to add other files in this folder with more API.
kodyvajjha pushed a commit that referenced this pull request Sep 22, 2023
Last prerequisite for Rademacher theorem in #7003.

Along the way, we weaken the second-countability assumptions for strong measurability of the derivative and the right derivative.
@ghost ghost removed the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Oct 2, 2023
@sgouezel sgouezel added awaiting-review and removed WIP Work in progress labels Oct 3, 2023
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sgouezel commented Oct 3, 2023

I have streamlined the Fubini argument, by using instead a general argument done in #7252. It's not clear to me that the bors d+ by @urkud still applies, so I am putting this back to awaiting-review.

sgouezel and others added 2 commits October 3, 2023 09:28
Co-authored-by: Rémy Degenne <remydegenne@gmail.com>
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Thanks!
bors r+

@github-actions github-actions bot added ready-to-merge This PR has been sent to bors. and removed awaiting-review labels Oct 6, 2023
bors bot pushed a commit that referenced this pull request Oct 6, 2023
We prove Rademacher theorem, stating that a Lipschitz function between finite-dimensional real vector spaces is differentiable almost everywhere.
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bors bot commented Oct 6, 2023

Build failed:

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bors retry

bors bot pushed a commit that referenced this pull request Oct 6, 2023
We prove Rademacher theorem, stating that a Lipschitz function between finite-dimensional real vector spaces is differentiable almost everywhere.
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bors bot commented Oct 6, 2023

This PR was included in a batch that was canceled, it will be automatically retried

bors bot pushed a commit that referenced this pull request Oct 6, 2023
We prove Rademacher theorem, stating that a Lipschitz function between finite-dimensional real vector spaces is differentiable almost everywhere.
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bors bot commented Oct 6, 2023

Pull request successfully merged into master.

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@bors bors bot changed the title feat: Rademacher theorem [Merged by Bors] - feat: Rademacher theorem Oct 6, 2023
@bors bors bot closed this Oct 6, 2023
@bors bors bot deleted the rademacher branch October 6, 2023 15:58
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5 participants