Theorems · Theorem · measure theory

Isometry.hausdorffMeasure_preimage

∀ {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 Y),
        (MeasureTheory.Measure.hausdorffMeasure d) (f ⁻¹' s) =
          (MeasureTheory.Measure.hausdorffMeasure d) (s ∩ Set.range f)

Defined in

Mathlib.MeasureTheory.Measure.Hausdorff

Cited by

2 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

EMetricSpaceEMetricSpaceMeasurableSpaceBorelSpaceMeasurableSpaceBorelSpace