Commit 2023-09-12 07:58 26bdb031

feat: add some lemmas for Haar measures (#7034) 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