Theorems · Theorem · general topology

HolderOnWith.ediam_image_le_of_subset_of_le

∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {C r : NNReal} {f : X → Y}
  {s t : Set X},
  HolderOnWith C r f s → t ⊆ s → ∀ {d : ENNReal}, Metric.ediam t ≤ d → Metric.ediam (f '' t) ≤ ↑C * d ^ ↑r

Defined in: Mathlib.Topology.MetricSpace.Holder
Cited by: 1 results in Mathlib
Foundations: Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PseudoEMetricSpace PseudoEMetricSpace

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Cites12

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

Setstatement and proof · cited by 53,352
Realstatement · cited by 25,697
ENNRealstatement and proof · cited by 9,879
Set.imagestatement · cited by 5,609
NNRealstatement and proof · cited by 4,310
PseudoEMetricSpacestatement and proof · cited by 1,536
ENNReal.ofNNRealstatement · cited by 1,279
NNReal.toRealstatement · cited by 1,260
Metric.ediamstatement and proof · cited by 159
HolderOnWithstatement and proof · cited by 44
HolderOnWith.monoproof · cited by 3
HolderOnWith.ediam_image_le_of_leproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

HolderOnWith.ediam_image_inter_le_of_leproof · cited by 1