Theorems · Theorem · measure theory

Isometry.hausdorffMeasure_image

∀ {X : Type u_2} {Y : Type u_3} [inst : EMetricSpace X] [inst_1 : EMetricSpace Y] [inst_2 : MeasurableSpace X]
  [inst_3 : BorelSpace X] [inst_4 : MeasurableSpace Y] [inst_5 : BorelSpace Y] {f : X → Y} {d : ℝ},
  Isometry f →
    0 ≤ d ∨ Function.Surjective f →
      ∀ (s : Set X), (MeasureTheory.Measure.hausdorffMeasure d) (f '' s) = (MeasureTheory.Measure.hausdorffMeasure d) s

Defined in

Mathlib.MeasureTheory.Measure.Hausdorff

Cited by

7 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

EMetricSpaceEMetricSpaceMeasurableSpaceBorelSpaceMeasurableSpaceBorelSpace