Theorems · Definition · dynamical systems
birkhoffSum
{α : Type u_1} → {M : Type u_2} → [AddCommMonoid M] → (α → α) → (α → M) → ℕ → α → MThe sum of values of g on the first n points of the orbit of x under f.
- Defined in
- Mathlib.Dynamics.BirkhoffSum.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumproof · cited by 5,195
- Finset.rangeproof · cited by 1,341
- Nat.iterateproof · cited by 740
Cited by21
Results whose statement or proof uses this declaration.
- birkhoffAverageproof · cited by 25
- dist_birkhoffAverage_birkhoffAveragestatement and proof · cited by 2
- birkhoffSum_apply_sub_birkhoffSumstatement and proof · cited by 2
- Function.IsFixedPt.birkhoffSum_eqstatement · cited by 1
- MeasureTheory.Measure.QuasiMeasurePreserving.birkhoffSum_ae_eq_of_ae_eqstatement · cited by 1
- dist_birkhoffSum_apply_birkhoffSumstatement and proof · cited by 1
- dist_birkhoffSum_birkhoffSum_lestatement · cited by 1
- map_birkhoffSumstatement · cited by 1
- map_birkhoffAverageproof · cited by 1
- birkhoffSum_of_comp_eqstatement · cited by 1
- birkhoffSum_onestatement · cited by 1
- birkhoffSum_one'statement · cited by 1