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

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

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feat(measure_theory/group/measure): Mapping an Haar measure under a l…
YaelDillies Nov 30, 2022
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continuous_linear_equiv version
YaelDillies Nov 30, 2022
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17 changes: 16 additions & 1 deletion src/measure_theory/group/measure.lean
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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 +716,21 @@ example {E : Type*} [normed_add_comm_group E] [normed_space ℝ E] [nontrivial E

end

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

instance map_continuous_linear_equiv.is_add_haar_measure (e : G ≃L[𝕜] H) :
is_add_haar_measure (μ.map e) :=
e.to_add_equiv.is_add_haar_measure_map _ e.continuous e.symm.continuous

variables [complete_space 𝕜] [t2_space G] [finite_dimensional 𝕜 G] [has_continuous_smul 𝕜 G]
[has_continuous_smul 𝕜 H]

instance map_linear_equiv.is_add_haar_measure (e : G ≃ₗ[𝕜] H) : is_add_haar_measure (μ.map e) :=
map_continuous_linear_equiv.is_add_haar_measure _ e.to_continuous_linear_equiv

end measure
end haar

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