Theorems · Theorem · general topology
eHolderNorm_eq_zero
∀ {X : Type u_1} {Y : Type u_2} [inst : MetricSpace X] [inst_1 : EMetricSpace Y] {r : NNReal} {f : X → Y},
eHolderNorm r f = 0 ↔ ∀ (x₁ x₂ : X), f x₁ = f x₂- Defined in
- Mathlib.Topology.MetricSpace.HolderNorm
- Cited by
- 1 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.
Cites28
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
- iInfproof · cited by 1,690
- MetricSpacestatement and proof · cited by 1,684
- PseudoEMetricSpaceproof · cited by 1,536
- ENNReal.ofNNRealproof · cited by 1,279
- NNReal.toRealproof · cited by 1,260
- LT.lt.neproof · cited by 872
- IsEmptyproof · cited by 759
- EDist.edistproof · cited by 735
- lt_of_le_of_ltproof · cited by 432
- Nonempty.someproof · cited by 340
Cited by1
Results whose statement or proof uses this declaration.
- MemHolder.nnHolderNorm_eq_zeroproof · cited by 0