Theorems · Theorem · measure theory

Isometry.euclideanHausdorffMeasure_preimage

∀ {X : Type u_1} {Y : Type u_2} [inst : EMetricSpace X] [inst_1 : MeasurableSpace X] [inst_2 : BorelSpace X]
  [inst_3 : EMetricSpace Y] [inst_4 : MeasurableSpace Y] [inst_5 : BorelSpace Y] {f : X → Y} {d : ℕ},
  Isometry f →
    ∀ (s : Set Y),
      (MeasureTheory.Measure.euclideanHausdorffMeasure d) (f ⁻¹' s) =
        (MeasureTheory.Measure.euclideanHausdorffMeasure d) (s ∩ Set.range f)

Defined in

Mathlib.Geometry.Euclidean.Volume.Measure

Cited by

0 results in Mathlib

Foundations

Depth 273 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

EMetricSpaceMeasurableSpaceBorelSpaceEMetricSpaceMeasurableSpaceBorelSpace