Theorems · Theorem · general topology
HolderWith.nnholderNorm_le
∀ {X : Type u_1} {Y : Type u_2} [inst : MetricSpace X] [inst_1 : EMetricSpace Y] {C r : NNReal} {f : X → Y},
HolderWith C r f → nnHolderNorm r f ≤ C- Defined in
- Mathlib.Topology.MetricSpace.HolderNorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 208 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealproof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- MetricSpacestatement and proof · cited by 1,684
- ENNReal.ofNNRealproof · cited by 1,279
- EMetricSpacestatement and proof · cited by 242
- ENNReal.coe_le_coeproof · cited by 73
- HolderWithstatement and proof · cited by 47
- nnHolderNormstatement · cited by 13
- HolderWith.memHolderproof · cited by 7
- MemHolder.coe_nnHolderNorm_eq_eHolderNormproof · cited by 5
- HolderWith.eHolderNorm_leproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- MemHolder.nnHolderNorm_add_leproof · cited by 1