Theorems · Theorem · general topology
lipschitzWith_iff_dist_le_mul
∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {K : NNReal} {f : α → β},
LipschitzWith K f ↔ ∀ (x y : α), dist (f x) (f y) ≤ ↑K * dist x y- Defined in
- Mathlib.Topology.MetricSpace.Lipschitz
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- ENNReal.ofNNRealproof · cited by 1,279
- NNReal.toRealstatement and proof · cited by 1,260
- LipschitzWithstatement · cited by 316
- NNDist.nndistproof · cited by 235
- edist_nndistproof · cited by 38
Cited by10
Results whose statement or proof uses this declaration.
- LipschitzWith.dist_le_mulproof · cited by 20
- LipschitzWith.of_dist_le_mulproof · cited by 13
- lipschitzWith_smulproof · cited by 5
- lipschitzWith_iff_norm_sub_leproof · cited by 2
- Real.lipschitzWith_toNNRealproof · cited by 2
- lipschitzWith_iff_norm_neg_add_leproof · cited by 1
- MeasureTheory.FiniteMeasure.testAgainstNN_lipschitzproof · cited by 1
- LipschitzWith.uniformly_boundedproof · cited by 1
- lipschitz_with_lipschitz_const_addproof · cited by 0
- lipschitz_with_lipschitz_const_mulproof · cited by 0