Theorems · Theorem · measure theory

MeasureTheory.lintegral_add_left_eq_self

∀ {G : Type u_1} [inst : MeasurableSpace G] {μ : MeasureTheory.Measure G} [inst_1 : AddGroup G] [MeasurableAdd G]
  [μ.IsAddLeftInvariant] (f : G → ENNReal) (g : G), ∫⁻ (x : G), f (g + x) ∂μ = ∫⁻ (x : G), f x ∂μ

Translating a function by left-addition 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

MeasurableSpaceAddGroupMeasurableAddMeasureTheory.Measure.IsAddLeftInvariant