Theorems · Theorem · general topology
memHolder_iff_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
- 0 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpaceEMetricSpace
Around this declaration
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement and proof · cited by 4,310
- MetricSpacestatement and proof · cited by 1,684
- EMetricSpacestatement and proof · cited by 242
- HolderWithstatement · cited by 47
- MemHolderstatement · cited by 26
- nnHolderNormstatement · cited by 13
- HolderWith.memHolderproof · cited by 7
- MemHolder.holderWithproof · cited by 7
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