Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

[Merged by Bors] - feat(measure_theory/group/measure): Mapping an Haar measure under a linear iso #17771

Closed
wants to merge 2 commits into from
Closed

[Merged by Bors] - feat(measure_theory/group/measure): Mapping an Haar measure under a linear iso #17771

Changes from 1 commit
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
6f113f6
feat(measure_theory/group/measure): Mapping an Haar measure under a l…
YaelDillies Nov 30, 2022
17acabb
continuous_linear_equiv version
YaelDillies Nov 30, 2022
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Jump to
Jump to file
Failed to load files.
Diff view
Diff view
12 changes: 11 additions & 1 deletion src/measure_theory/group/measure.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -30,7 +30,7 @@ noncomputable theory
open_locale ennreal pointwise big_operators topological_space
open has_inv set function measure_theory.measure filter

variables {G : Type*} [measurable_space G]
variables {𝕜 G H : Type*} [measurable_space G] [measurable_space H]

namespace measure_theory
namespace measure
Expand Down Expand Up @@ -716,6 +716,16 @@ example {E : Type*} [normed_add_comm_group E] [normed_space ℝ E] [nontrivial E

end

variables [nontrivially_normed_field 𝕜] [complete_space 𝕜] [topological_space G] [add_comm_group G]
[module 𝕜 G] [finite_dimensional 𝕜 G] [has_continuous_smul 𝕜 G] (μ : measure G)
[is_add_haar_measure μ] [borel_space G] [t2_space G] [topological_add_group G]
[topological_space H] [add_comm_group H] [module 𝕜 H] [finite_dimensional 𝕜 H]
[has_continuous_smul 𝕜 H] [borel_space H] [t2_space H] [topological_add_group H]

instance (e : G ≃ₗ[𝕜] H) : is_add_haar_measure (μ.map e) :=
e.to_add_equiv.is_add_haar_measure_map _ (e : G →ₗ[𝕜] H).continuous_of_finite_dimensional
(e.symm : H →ₗ[𝕜] G).continuous_of_finite_dimensional
Copy link
Member

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Is finite-dimensionality only used explicitly? If so, could you also add a version where e : G ≃L[𝕜] H without finite-dimensionality assumptions?

bors d+

Copy link
Collaborator

@sgouezel sgouezel Nov 30, 2022 •
edited

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Can you also use this to golf the proof of map_linear_map_add_haar_eq_smul_add_haar? (where an instance would become unnecessary, as well as a few facts like Ce or Cesymm only used to prove the instance).

Copy link
Collaborator Author

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

I will golf map_linear_map_add_haar_eq_smul_add_haar separately because I have more API incoming that will shorten it.

bors merge


end measure
end haar

Expand Down