[Merged by Bors] - feat: Rademacher theorem #7003
Closed
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
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.
leanprover-community-mathlib4-bot
removed
the
blocked-by-other-PR
sgouezel
added
awaiting-review
RemyDegenne
reviewed
Oct 3, 2023
RemyDegenne
reviewed
Oct 3, 2023
Co-authored-by: Rémy Degenne <remydegenne@gmail.com>
![github-actions[bot]](https://avatars.githubusercontent.com/in/15368?s=60&v=4){kind=small}
|
Thanks! |
github-actions
bot
added
ready-to-merge
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.
|
Build failed: |
|
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.
|
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.
|
Pull request successfully merged into master. Build succeeded! The publicly hosted instance of bors-ng is deprecated and will go away soon. If you want to self-host your own instance, instructions are here. If you want to switch to GitHub's built-in merge queue, visit their help page. |
bors
bot
changed the title
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
We prove Rademacher theorem, stating that a Lipschitz function between finite-dimensional real vector spaces is differentiable almost everywhere.