Theorems · Theorem · measure theory

MeasureTheory.lintegral_mul_left_eq_self

∀ {G : Type u_1} [inst : MeasurableSpace G] {μ : MeasureTheory.Measure G} [inst_1 : Group G] [MeasurableMul G]
  [μ.IsMulLeftInvariant] (f : G → ENNReal) (g : G), ∫⁻ (x : G), f (g * x) ∂μ = ∫⁻ (x : G), f x ∂μ

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

Defined in

Mathlib.MeasureTheory.Group.LIntegral

Cited by

4 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceGroupMeasurableMulMeasureTheory.Measure.IsMulLeftInvariant