Theorems · Theorem · measure theory

MeasureTheory.Measure.setIntegral_comp_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] {F : Type u_2}
  [inst_6 : NormedAddCommGroup F] [inst_7 : NormedSpace ℝ F] (f : E → F) {R : ℝ} (s : Set E),
  R ≠ 0 → ∫ (x : E) in s, f (R • x) ∂μ = |(R ^ Module.finrank ℝ E)⁻¹| • ∫ (x : E) in R • s, f x ∂μ

Defined in

Mathlib.MeasureTheory.Measure.Haar.NormedSpace

Cited by

1 results in Mathlib

Foundations

Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceFiniteDimensionalMeasureTheory.Measure.IsAddHaarMeasureNormedAddCommGroupNormedSpace