Theorems · Theorem · general topology
HolderOnWith.edist_le
∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {C r : NNReal} {f : X → Y}
{s : Set X}, HolderOnWith C r f s → ∀ {x y : X}, x ∈ s → y ∈ s → edist (f x) (f y) ≤ ↑C * edist x y ^ ↑r- Defined in
- Mathlib.Topology.MetricSpace.Holder
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 201 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.
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- ENNRealstatement · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealstatement · cited by 1,279
- NNReal.toRealstatement · cited by 1,260
- EDist.ediststatement · cited by 735
- HolderOnWithstatement and proof · cited by 44
Cited by4
Results whose statement or proof uses this declaration.
- HolderOnWith.edist_le_of_leproof · cited by 4
- HolderOnWith.monoproof · cited by 3
- HolderOnWith.compproof · cited by 2
- HolderOnWith.uniformContinuousOnproof · cited by 2