Theorems · Theorem · general topology

HolderOnWith.ediam_image_le_of_le

∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {C r : NNReal} {f : X → Y}
  {s : Set X}, HolderOnWith C r f s → ∀ {d : ENNReal}, Metric.ediam s ≤ d → Metric.ediam (f '' s) ≤ ↑C * d ^ ↑r

Defined in

Mathlib.Topology.MetricSpace.Holder

Cited by

2 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpace