[Merged by Bors] - feat: extend results on product measures from sigma-finite to s-finite measures#8713
Closed
[Merged by Bors] - feat: extend results on product measures from sigma-finite to s-finite measures#8713
Conversation
Contributor
sgouezel
commented
Nov 29, 2023
Member
|
I'll come to the office in ~40min and review from there. |
urkud
reviewed
Nov 29, 2023
urkud
reviewed
Nov 29, 2023
urkud
reviewed
Nov 29, 2023
| classical | ||
| obtain ⟨f, hf⟩ : ∃ f : ι → ℕ, Function.Injective f := Countable.exists_injective_nat ι | ||
| let e : ι ≃ range f := Equiv.ofInjective f hf | ||
| let m' : ℕ → Measure α := fun n ↦ if hn : n ∈ range f then m (e.symm ⟨n, hn⟩) else 0 |
Member
There was a problem hiding this comment.
I see 2 ways to move parts of this proof to reusable lemmas.
- Add
Measure.sum_comp_equiv, instances forIsFiniteMeasure (∑ i, f i)and[Finite ι] : IsFiniteMeasure (.sum f), then treat[Finite ι]and[Infinite ι]separately. - Add
Measure.sum_extend_zerousingFunction.extendinstead of the equivalent definition you use, then apply it.
Maybe, we should have all these supporting lemmas/instances.
Contributor
Author
There was a problem hiding this comment.
I have added Measure.sum_comp_equiv and Measure.sum_extend_zero. Indeed, the proof becomes nicer with these! On the other hand, I don't think that splitting into finite or infinite \iota would make things nicer.
Member
There was a problem hiding this comment.
I generalized sum_extend_zero and Function.apply_extend.
bors d+
- `Function.apply_extend` doesn't need any assumptions on `f`. - Add `tsum_extend_zero`. - Generalize `sum_extend_zero` to any injective function, not just `Subtype.val`. - Use it to golf `sfinite_sum_of_countable`.
Contributor
|
✌️ sgouezel can now approve this pull request. To approve and merge a pull request, simply reply with |
Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
Contributor
Author
|
bors r+ |
mathlib-bors bot
pushed a commit
that referenced
this pull request
Dec 1, 2023
…e measures (#8713) Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
mathlib-bors bot
pushed a commit
that referenced
this pull request
Dec 1, 2023
…e measures (#8713) Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
Contributor
|
Pull request successfully merged into master. Build succeeded: |
awueth
pushed a commit
that referenced
this pull request
Dec 19, 2023
…e measures (#8713) Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
This file contains hidden or 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
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
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.