Theorems · Theorem · dynamical systems
birkhoffSum_one
∀ {α : Type u_1} {M : Type u_2} [inst : AddCommMonoid M] (f : α → α) (g : α → M) (x : α), birkhoffSum f g 1 x = g x- Defined in
- Mathlib.Dynamics.BirkhoffSum.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 56 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
- Nat.iterateproof · cited by 740
- birkhoffSumstatement · cited by 20
- Finset.sum_range_oneproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- birkhoffSum_one'proof · cited by 1