Theorems · Theorem · measure theory

MeasureTheory.Measure.addHaar_smul

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E] [BorelSpace E]
  [FiniteDimensional ℝ E] (μ : MeasureTheory.Measure E) [μ.IsAddHaarMeasure] (r : ℝ) (s : Set E),
  μ (r • s) = ENNReal.ofReal |r ^ Module.finrank ℝ E| * μ s

Rescaling a set by a factor r multiplies its measure by abs (r ^ dim).

Defined in

Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar

Cited by

13 results in Mathlib

Foundations

Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceFiniteDimensionalMeasureTheory.Measure.IsAddHaarMeasure