Theorems · Theorem · general topology
holderOnWith_one
∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {C : NNReal} {f : X → Y}
{s : Set X}, HolderOnWith C 1 f s ↔ LipschitzOnWith C f s- Defined in
- Mathlib.Topology.MetricSpace.Holder
- Cited by
- 2 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.
Cites8
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
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealproof · cited by 1,279
- EDist.edistproof · cited by 735
- LipschitzOnWithstatement · cited by 164
- ENNReal.rpow_oneproof · cited by 56
- HolderOnWithstatement · cited by 44
Cited by2
Results whose statement or proof uses this declaration.
- LipschitzOnWith.holderOnWithproof · cited by 2
- holderWith_oneproof · cited by 1