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Theorems · Theorem · general topology

MemHolder.eHolderNorm_lt_top

∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {r : NNReal} {f : X → Y},
  MemHolder r f → eHolderNorm r f < ⊤

Alias of the reverse direction of eHolderNorm_lt_top.

Defined in
Mathlib.Topology.MetricSpace.HolderNorm
Cited by
2 results in Mathlib
Foundations
Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpacePseudoEMetricSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MemHolder.holderWith · cited by 7MemHolder.holderWitheHolderNorm_smul · cited by 2eHolderNorm_smulENNReal · cited by 9879ENNRealTop.top · cited by 9680Top.topNNReal · cited by 4310NNRealPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceMemHolder · cited by 26MemHoldereHolderNorm · cited by 16eHolderNormeHolderNorm_lt_top · cited by 2eHolderNorm_lt_topMemHolder.eHolderNorm_lt_topCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.