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[Merged by Bors] - feat(measure_theory): image of Lebesgue measure under shift/rescale #3760

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@urkud urkud commented Aug 13, 2020


Depends on #3757 #3758 #3759

Add lemmas `preimage_mul_const_Ixx` and `preimage_const_mul_Ixx`.
Other changes:

* `to_units` doesn't work with `to_additive`, so move the `to_fun`
part to `units.mk'`.
* Generalize `equiv.mul_left` and `equiv.mul_right` to `units`.
@urkud urkud added blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. WIP Work in progress labels Aug 13, 2020
This went to #3756, not needed for the rest of PR
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This is great! You have some ext lemmas that were nicer than mine, but I generalized the last special case a bit, without giving up (much) usability.

Note: not all lemmas about =ᵐ consistently use ae_eq, some use eventually_eq (this can be fixed in a different PR).

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@@ -1049,7 +1233,13 @@ class probability_measure (μ : measure α) : Prop := (measure_univ : μ univ =
/-- A measure `μ` is called finite if `μ univ < ⊤`. -/
class finite_measure (μ : measure α) : Prop := (measure_univ_lt_top : μ univ < ⊤)

export probability_measure (measure_univ)
/-- Measure `μ` *has no atoms* if the measure of each singleton is zero.-/
class no_atoms_measure (μ : measure α) : Prop :=
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I think I would prefer the name has_no_atoms instead.

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I've also seen the term continuous measure for this property. The doc-string should mention this term.

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Renamed. Feel free to add "continuous measure" to the doc string. I don't want to do it myself because I never saw it (only "absolutely continuous" but this is a different property). I also commented on the definition. I don't want to change it in this PR but probably we should do it in the future.

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@fpvandoorn fpvandoorn added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels Aug 22, 2020
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urkud and others added 2 commits September 3, 2020 10:51
Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>
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What is the status of this PR? Are you still working on the review comments?

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urkud commented Sep 14, 2020

I'm sorry for the delay. I'll push update in about 1 hour.

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Thanks for the fixes.

bors r+

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bors bot commented Sep 14, 2020

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(measure_theory): image of Lebesgue measure under shift/rescale [Merged by Bors] - feat(measure_theory): image of Lebesgue measure under shift/rescale Sep 14, 2020
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@bors bors bot deleted the integral-map branch September 14, 2020 21:25
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3 participants