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[Merged by Bors] - feat: add some lemmas for Haar measures #7034

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[Merged by Bors] - feat: add some lemmas for Haar measures #7034

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@xroblot xroblot commented Sep 8, 2023 •
edited by eric-wieser
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We prove some lemmas that will be useful in following PRs #6832 and #7037, mainly:

theorem Basis.addHaar_eq {b : Basis ι ℝ E} {b' : Basis ι' ℝ E} :
     b.addHaar = b'.addHaar ↔ b.addHaar b'.parallelepiped = 1

theorem Basis.parallelepiped_eq_map (b : Basis ι ℝ E) :
     b.parallelepiped = (TopologicalSpace.PositiveCompacts.piIcc01 ι).map b.equivFun.symm
       b.equivFunL.symm.continuous

theorem Basis.addHaar_map (b : Basis ι ℝ E) (f : E ≃L[ℝ] F) :
    map f b.addHaar = (b.map f.toLinearEquiv).addHaar

Co-authored-by: Eric Wieser [email protected]

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@xroblot xroblot added WIP Work in progress t-measure-probability Measure theory / Probability theory awaiting-CI labels Sep 8, 2023
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@xroblot xroblot changed the title Add some lemmas for Haar measures feat: add some lemmas for Haar measures Sep 8, 2023
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Thanks!

bors d+

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✌️ xroblot can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

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xroblot commented Sep 12, 2023

bors r+

bors bot pushed a commit that referenced this pull request Sep 12, 2023
@xroblot @eric-wieser
feat: add some lemmas for Haar measures (#7034)
bbc0bc5 
We prove some lemmas that will be useful in following PRs #6832 and #7037, mainly:
```lean
theorem Basis.addHaar_eq {b : Basis ι ℝ E} {b' : Basis ι' ℝ E} :
     b.addHaar = b'.addHaar ↔ b.addHaar b'.parallelepiped = 1

theorem Basis.parallelepiped_eq_map (b : Basis ι ℝ E) :
     b.parallelepiped = (TopologicalSpace.PositiveCompacts.piIcc01 ι).map b.equivFun.symm
       b.equivFunL.symm.continuous

theorem Basis.addHaar_map (b : Basis ι ℝ E) (f : E ≃L[ℝ] F) :
    map f b.addHaar = (b.map f.toLinearEquiv).addHaar
```

Co-authored-by: Eric Wieser <[email protected]>
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bors bot pushed a commit that referenced this pull request Sep 12, 2023
@xroblot @eric-wieser
feat: add some lemmas for Haar measures (#7034)
26bdb03 
We prove some lemmas that will be useful in following PRs #6832 and #7037, mainly:
```lean
theorem Basis.addHaar_eq {b : Basis ι ℝ E} {b' : Basis ι' ℝ E} :
     b.addHaar = b'.addHaar ↔ b.addHaar b'.parallelepiped = 1

theorem Basis.parallelepiped_eq_map (b : Basis ι ℝ E) :
     b.parallelepiped = (TopologicalSpace.PositiveCompacts.piIcc01 ι).map b.equivFun.symm
       b.equivFunL.symm.continuous

theorem Basis.addHaar_map (b : Basis ι ℝ E) (f : E ≃L[ℝ] F) :
    map f b.addHaar = (b.map f.toLinearEquiv).addHaar
```

Co-authored-by: Eric Wieser <[email protected]>
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@bors bors bot changed the title feat: add some lemmas for Haar measures [Merged by Bors] - feat: add some lemmas for Haar measures Sep 12, 2023
@bors bors bot closed this Sep 12, 2023
@bors bors bot deleted the xfr_haartools branch September 12, 2023 08:18
kodyvajjha pushed a commit that referenced this pull request Sep 22, 2023
@xroblot @eric-wieser @kodyvajjha
feat: add some lemmas for Haar measures (#7034)
01a1e92 
We prove some lemmas that will be useful in following PRs #6832 and #7037, mainly:
```lean
theorem Basis.addHaar_eq {b : Basis ι ℝ E} {b' : Basis ι' ℝ E} :
     b.addHaar = b'.addHaar ↔ b.addHaar b'.parallelepiped = 1

theorem Basis.parallelepiped_eq_map (b : Basis ι ℝ E) :
     b.parallelepiped = (TopologicalSpace.PositiveCompacts.piIcc01 ι).map b.equivFun.symm
       b.equivFunL.symm.continuous

theorem Basis.addHaar_map (b : Basis ι ℝ E) (f : E ≃L[ℝ] F) :
    map f b.addHaar = (b.map f.toLinearEquiv).addHaar
```

Co-authored-by: Eric Wieser <[email protected]>
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