Theorems · Theorem · measure theory

Isometry.map_euclideanHausdorffMeasure

∀ {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 →
    MeasureTheory.Measure.map f (MeasureTheory.Measure.euclideanHausdorffMeasure d) =
      (MeasureTheory.Measure.euclideanHausdorffMeasure d).restrict (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: EMetricSpace MeasurableSpace BorelSpace EMetricSpace MeasurableSpace BorelSpace

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

MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Set.rangestatement and proof · cited by 4,705
MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
BorelSpacestatement and proof · cited by 1,602
MeasureTheory.MeasureSpace.volumeproof · cited by 1,323
MeasureTheory.Measure.mapstatement and proof · cited by 858
EMetricSpacestatement and proof · cited by 242
Isometrystatement and proof · cited by 230
MeasureTheory.Measure.hausdorffMeasureproof · cited by 71
MeasureTheory.Measure.addHaarScalarFactorproof · cited by 58
MeasureTheory.Measure.euclideanHausdorffMeasurestatement · cited by 21

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