Theorems · Theorem · Lie groups

MeasureTheory.forall_measure_preimage_mul_iff

∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : Mul G] [MeasurableMul G] (μ : MeasureTheory.Measure G),
  (∀ (g : G) (A : Set G), MeasurableSet A → μ ((fun h => g * h) ⁻¹' A) = μ A) ↔ μ.IsMulLeftInvariant

An alternative way to prove that μ is left invariant under multiplication.

Defined in

Mathlib.MeasureTheory.Group.Measure

Cited by

1 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMulMeasurableMul