Theorems · Theorem · measure theory

MeasureTheory.integral_mul_right_eq_self

∀ {G : Type u_4} {E : Type u_5} [inst : MeasurableSpace G] [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace ℝ E]
  {μ : MeasureTheory.Measure G} [inst_3 : Group G] [MeasurableMul G] [μ.IsMulRightInvariant] (f : G → E) (g : G),
  ∫ (x : G), f (x * g) ∂μ = ∫ (x : G), f x ∂μ

Translating a function by right-multiplication does not change its integral with respect to a right-invariant measure.

Defined in

Mathlib.MeasureTheory.Group.Integral

Cited by

3 results in Mathlib

Foundations

Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceNormedAddCommGroupNormedSpaceGroupMeasurableMulMeasureTheory.Measure.IsMulRightInvariant