Theorems · Theorem · dynamical systems
Function.IsFixedPt.birkhoffAverage_eq
∀ (R : Type u_1) {α : Type u_2} {M : Type u_3} [inst : DivisionSemiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] {f : α → α} {x : α},
Function.IsFixedPt f x → ∀ (g : α → M) {n : ℕ}, ↑n ≠ 0 → birkhoffAverage R f g n x = g x- Defined in
- Mathlib.Dynamics.BirkhoffSum.Average
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- DivisionSemiringstatement and proof · cited by 216
- Nat.cast_smul_eq_nsmulproof · cited by 110
- Function.IsFixedPtstatement and proof · cited by 84
- inv_smul_smul₀proof · cited by 80
- birkhoffAveragestatement · cited by 25
- Function.IsFixedPt.birkhoffSum_eqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Function.IsFixedPt.tendsto_birkhoffAverageproof · cited by 1