Theorems · Theorem · Lie groups

MeasureTheory.measure_preimage_add

∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : AddGroup G] [MeasurableAdd G] (μ : MeasureTheory.Measure G)
  [μ.IsAddLeftInvariant] (g : G) (A : Set G), μ ((fun h => g + h) ⁻¹' A) = μ A

We shorten this from measure_preimage_add_left, since left invariant is the preferred option for measures in this formalization.

Defined in

Mathlib.MeasureTheory.Group.Measure

Cited by

14 results in Mathlib

Foundations

Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceAddGroupMeasurableAddMeasureTheory.Measure.IsAddLeftInvariant