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110f4f3 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 | import Mathlib
import OAI.Analysis.BiholderTransport.Model
namespace OAI
section
section
noncomputable section
open Set Filter Manifold Bundle Module
open scoped Topology ContDiff
namespace WeakMTWTransport
section FixedJoinSpectrum
variable {n : ℕ} {M : Type*} [MetricSpace M] [ChartedSpace (Model n) M]
local instance tangentFiniteSpectrum (x : M) :
FiniteDimensional ℝ (TangentSpace 𝓘(ℝ,Model n) x) :=
inferInstanceAs (FiniteDimensional ℝ (Model n))
lemma tangent_finrank (x : M) : finrank ℝ (TangentSpace 𝓘(ℝ,Model n) x)=n :=
finrank_euclideanSpace_fin
end FixedJoinSpectrum
end WeakMTWTransport
end
end
section
noncomputable section
open Set Filter Manifold Bundle
open scoped Topology ContDiff
namespace WeakMTWTransport
section EndpointJoinAction
variable {n : ℕ} {M : Type*} [MetricSpace M] [CompactSpace M]
[ChartedSpace (Model n) M] [IsManifold 𝓘(ℝ,Model n) ∞ M]
[RiemannianBundle (fun x : M => TangentSpace 𝓘(ℝ,Model n) x)]
[IsContMDiffRiemannianBundle 𝓘(ℝ,Model n) ∞ (Model n)
(fun x : M => TangentSpace 𝓘(ℝ,Model n) x)]
[IsRiemannianManifold 𝓘(ℝ,Model n) M]
local instance tangentFiniteEndpointJoin (x : M) :
FiniteDimensional ℝ (TangentSpace 𝓘(ℝ,Model n) x) :=
inferInstanceAs (FiniteDimensional ℝ (Model n))
end EndpointJoinAction
end WeakMTWTransport
end
end
end
end OAI
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