Theorems · Theorem · general topology
MemHolder.coe_nnHolderNorm_eq_eHolderNorm
∀ {X : Type u_1} {Y : Type u_2} [inst : MetricSpace X] [inst_1 : EMetricSpace Y] {r : NNReal} {f : X → Y},
MemHolder r f → ↑(nnHolderNorm r f) = eHolderNorm r f- Defined in
- Mathlib.Topology.MetricSpace.HolderNorm
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 207 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- MetricSpacestatement and proof · cited by 1,684
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- lt_of_le_of_ltproof · cited by 432
- EMetricSpacestatement and proof · cited by 242
- ne_of_ltproof · cited by 203
- ENNReal.coe_toNNRealproof · cited by 53
- ENNReal.coe_lt_topproof · cited by 52
- MemHolderstatement and proof · cited by 26
- eHolderNormstatement and proof · cited by 16
- nnHolderNormstatement · cited by 13
Cited by5
Results whose statement or proof uses this declaration.
- eHolderNorm_smulproof · cited by 2
- MemHolder.nnHolderNorm_smulproof · cited by 1
- HolderWith.nnholderNorm_leproof · cited by 1
- eHolderNorm_add_leproof · cited by 0
- MemHolder.nnHolderNorm_eq_zeroproof · cited by 0