Theorems · Definition · general topology
MemHolder
{X : Type u_1} → {Y : Type u_2} → [PseudoEMetricSpace X] → [PseudoEMetricSpace Y] → NNReal → (X → Y) → PropA function f is MemHolder r f if it is Hölder continuous. Namely, f has a finite
r-Hölder constant. This is equivalent to f having finite Hölder norm.
c.f. memHolder_iff.
- Defined in
- Mathlib.Topology.MetricSpace.HolderNorm
- Cited by
- 26 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.
Cites3
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
- HolderWithproof · cited by 47
Cited by26
Results whose statement or proof uses this declaration.
- MemHolder.holderWithstatement and proof · cited by 7
- HolderWith.memHolderstatement · cited by 7
- MemHolder.coe_nnHolderNorm_eq_eHolderNormstatement and proof · cited by 5
- MemHolder.smulstatement and proof · cited by 4
- MemHolder.of_lestatement and proof · cited by 3
- MemHolder.addstatement and proof · cited by 2
- MemHolder.eHolderNorm_lt_topstatement · cited by 2
- memHolder_conststatement · cited by 2
- eHolderNorm_eq_topstatement · cited by 2
- eHolderNorm_lt_topstatement and proof · cited by 2
- eHolderNorm_ne_topstatement · cited by 2
- eHolderNorm_smulproof · cited by 2