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

Use Type* instead of Type _ as recommended #11

Merged
merged 1 commit into from
Feb 29, 2024
Merged

Use Type* instead of Type _ as recommended #11

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
2 changes: 1 addition & 1 deletion BET/Birkhoff.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -27,7 +27,7 @@ open BigOperators MeasureTheory
- `T` is a measure preserving map of a probability space `(α, μ)`,
- `f g : α → ℝ` are integrable.
-/
variable {α : Type _} [MeasurableSpace α]
variable {α : Type*} [MeasurableSpace α]
variable {μ : MeasureTheory.Measure α} [MeasureTheory.IsProbabilityMeasure μ]
variable {T : α → α} (hT : MeasurePreserving T μ)
variable {f g : α → ℝ} (hf : Integrable f μ) (hg : Integrable g μ)
Expand Down
4 changes: 2 additions & 2 deletions BET/Topological.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -26,7 +26,7 @@ set_option autoImplicit false

section Topological_Dynamics

variable {α : Type _} [MetricSpace α]
variable {α : Type*} [MetricSpace α]

/-- The non-wandering set of `f` is the set of points which return arbitrarily close after some iterate. -/
def nonWanderingSet (f : α → α) : Set α :=
Expand Down Expand Up @@ -336,7 +336,7 @@ theorem nonWandering_nonempty [hα : Nonempty α] : Set.Nonempty (nonWanderingSe


/-- The recurrent set is the set of points that are recurrent, i.e. that belong to their omega-limit set. -/
def recurrentSet {α : Type _} [TopologicalSpace α] (f : α → α) : Set α :=
def recurrentSet {α : Type*} [TopologicalSpace α] (f : α → α) : Set α :=
{ x | x ∈ ω⁺ (fun n ↦ f^[n]) ({x}) }

theorem recurrentSet_iff_accumulation_point (x : α) :
Expand Down