[Merged by Bors] - feat(measure_theory/order/upper_lower): Order-connected sets in ℝⁿ are measurable
#16976
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
YaelDillies
added
awaiting-review
sgouezel
reviewed
Oct 14, 2022
upper sets form a monoid upper set of open is open antichains have measure zero
github-actions
bot
added
the
modifies-synchronized-file
YaelDillies
added
not-too-late
YaelDillies
force-pushed
the
ord_connected_measurable
branch
from
de2d60b
to
74370c4
Compare
|
✌️ YaelDillies can now approve this pull request. To approve and merge a pull request, simply reply with |
leanprover-community-bot-assistant
added
delegated
|
bors merge |
|
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
ℝⁿ are measurableℝⁿ are measurable
mathlib-bors bot
pushed a commit
to leanprover-community/mathlib4
that referenced
this pull request
Feb 14, 2024
* Add `upperBounds_closure`, `lowerBounds_closure`, `bddAbove_closure`, `bddBelow_closure`. * Add `IsAntichain.interior_eq_empty`. * Generalize `nhds_left'_le_nhds_ne` and `nhds_right'_le_nhds_ne` to a `Preorder`. Partly forward-ports leanprover-community/mathlib#16976
1 task
riccardobrasca
pushed a commit
to leanprover-community/mathlib4
that referenced
this pull request
Feb 18, 2024
* Add `upperBounds_closure`, `lowerBounds_closure`, `bddAbove_closure`, `bddBelow_closure`. * Add `IsAntichain.interior_eq_empty`. * Generalize `nhds_left'_le_nhds_ne` and `nhds_right'_le_nhds_ne` to a `Preorder`. Partly forward-ports leanprover-community/mathlib#16976
dagurtomas
pushed a commit
to leanprover-community/mathlib4
that referenced
this pull request
Mar 22, 2024
* Add `upperBounds_closure`, `lowerBounds_closure`, `bddAbove_closure`, `bddBelow_closure`. * Add `IsAntichain.interior_eq_empty`. * Generalize `nhds_left'_le_nhds_ne` and `nhds_right'_le_nhds_ne` to a `Preorder`. Partly forward-ports leanprover-community/mathlib#16976
YaelDillies
added a commit
to leanprover-community/mathlib4
that referenced
this pull request
Mar 23, 2024
Partially forward-port leanprover-community/mathlib#16976
mathlib-bors bot
pushed a commit
to leanprover-community/mathlib4
that referenced
this pull request
Mar 23, 2024
Partially forward-port leanprover-community/mathlib#16976 Also fix an unused argument that somehow made it to master, likely from #10661.
utensil
pushed a commit
to leanprover-community/mathlib4
that referenced
this pull request
Mar 26, 2024
Partially forward-port leanprover-community/mathlib#16976 Also fix an unused argument that somehow made it to master, likely from #10661.
Louddy
pushed a commit
to leanprover-community/mathlib4
that referenced
this pull request
Apr 15, 2024
Partially forward-port leanprover-community/mathlib#16976 Also fix an unused argument that somehow made it to master, likely from #10661.
atarnoam
pushed a commit
to leanprover-community/mathlib4
that referenced
this pull request
Apr 16, 2024
Partially forward-port leanprover-community/mathlib#16976 Also fix an unused argument that somehow made it to master, likely from #10661.
uniwuni
pushed a commit
to leanprover-community/mathlib4
that referenced
this pull request
Apr 19, 2024
Partially forward-port leanprover-community/mathlib#16976 Also fix an unused argument that somehow made it to master, likely from #10661.
callesonne
pushed a commit
to leanprover-community/mathlib4
that referenced
this pull request
Apr 22, 2024
Partially forward-port leanprover-community/mathlib#16976 Also fix an unused argument that somehow made it to master, likely from #10661.
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.
Prove that the frontier of an order-connected set in
ℝⁿ(with the∞-metric, but it doesn't actually matter) has measure zero.As a corollary, antichains in
ℝⁿhave measure zero.Co-authored-by: @JasonKYi
ennreal.of_real#16955nhds_withinversions #16956a * b ≠ b ↔ a ≠ 1#18635This is a three lines remark in Reverse Kleitman Inequalities, Bollobas, Leader, Radcliffe, with no proof. So Jason, Bhavik and I came up with a proof using Lebesgue Density Theorem.