Theorems · Theorem · general topology
eHolderNorm_of_isEmpty
∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {r : NNReal} {f : X → Y}
[hX : IsEmpty X], eHolderNorm r f = 0- Defined in
- Mathlib.Topology.MetricSpace.HolderNorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Bot.botproof · cited by 4,720
- NNRealstatement and proof · cited by 4,310
- iInfproof · cited by 1,690
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealproof · cited by 1,279
- IsEmptystatement and proof · cited by 759
- HolderWithproof · cited by 47
- eHolderNormstatement · cited by 16
- ENNReal.bot_eq_zeroproof · cited by 5
- iInf₂_eq_botproof · cited by 4
- HolderWith.of_isEmptyproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- eHolderNorm_eq_zeroproof · cited by 1