Theorems · Theorem · dynamical systems
dist_birkhoffSum_apply_birkhoffSum
∀ {α : Type u_1} {E : Type u_2} [inst : NormedAddCommGroup E] (f : α → α) (g : α → E) (n : ℕ) (x : α),
dist (birkhoffSum f g n (f x)) (birkhoffSum f g n x) = dist (g (f^[n] x)) (g x)- Defined in
- Mathlib.Dynamics.BirkhoffSum.NormedSpace
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
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.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Norm.normproof · cited by 5,413
- Dist.diststatement · cited by 1,539
- Nat.iteratestatement and proof · cited by 740
- dist_eq_normproof · cited by 182
- birkhoffSumstatement and proof · cited by 20
- birkhoffSum_apply_sub_birkhoffSumproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- dist_birkhoffAverage_apply_birkhoffAverageproof · cited by 1