Theorems · Theorem · measure theory

WithLp.volume_preserving_symm_measurableEquiv_toLp_prod

∀ (U : Type u_4) (V : Type u_5) [inst : NormedAddCommGroup U] [inst_1 : InnerProductSpace ℝ U]
  [inst_2 : MeasurableSpace U] [inst_3 : BorelSpace U] [inst_4 : FiniteDimensional ℝ U] [inst_5 : NormedAddCommGroup V]
  [inst_6 : InnerProductSpace ℝ V] [inst_7 : MeasurableSpace V] [inst_8 : BorelSpace V]
  [inst_9 : FiniteDimensional ℝ V],
  MeasureTheory.MeasurePreserving (⇑(MeasurableEquiv.toLp 2 (U × V)).symm) MeasureTheory.volume MeasureTheory.volume

The measure equivalence between WithLp 2 (U × V) and U × V is volume preserving.

Defined in

Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace

Cited by

2 results in Mathlib

Foundations

Depth 266 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMeasurableSpaceBorelSpaceFiniteDimensionalNormedAddCommGroupInnerProductSpaceMeasurableSpaceBorelSpaceFiniteDimensional