Theorems · Theorem · general topology
MemHolder.holderWith
∀ {X : Type u_1} {Y : Type u_2} [inst : MetricSpace X] [inst_1 : EMetricSpace Y] {r : NNReal} {f : X → Y},
MemHolder r f → HolderWith (nnHolderNorm r f) r f- Defined in
- Mathlib.Topology.MetricSpace.HolderNorm
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpaceEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealproof · cited by 9,879
- Top.topproof · cited by 9,680
- NNRealstatement and proof · cited by 4,310
- MetricSpacestatement and proof · cited by 1,684
- ENNReal.ofNNRealproof · cited by 1,279
- NNReal.toRealproof · cited by 1,260
- LT.lt.neproof · cited by 872
- EDist.edistproof · cited by 735
- EMetricSpacestatement and proof · cited by 242
- ne_of_ltproof · cited by 203
- ENNReal.toNNRealproof · cited by 165
- le_iInf₂proof · cited by 67
Cited by7
Results whose statement or proof uses this declaration.
- MemHolder.coe_nnHolderNorm_eq_eHolderNormproof · cited by 5
- MemHolder.smulproof · cited by 4
- MemHolder.addproof · cited by 2
- eHolderNorm_smulproof · cited by 2
- MemHolder.nnHolderNorm_add_leproof · cited by 1
- memHolder_iff_holderWithproof · cited by 0
- MemHolder.compproof · cited by 0