Theorems · Theorem · general topology
LipschitzWith.iterate
∀ {α : Type u} [inst : PseudoEMetricSpace α] {K : NNReal} {f : α → α},
LipschitzWith K f → ∀ (n : ℕ), LipschitzWith (K ^ n) f^[n]Iterates of a Lipschitz function are Lipschitz.
- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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.
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Nat.iteratestatement · cited by 740
- LipschitzWithstatement and proof · cited by 316
Cited by4
Results whose statement or proof uses this declaration.
- LipschitzWith.dist_iterate_succ_le_geometricproof · cited by 2
- uniformEquicontinuous_birkhoffAverageproof · cited by 1
- LinearMap.tendsto_birkhoffAverage_of_ker_subset_closureproof · cited by 1
- LipschitzWith.edist_iterate_succ_le_geometricproof · cited by 1