G : Type u_1
inst✝⁶ : MeasurableSpace G
inst✝⁵ : Group G
inst✝⁴ : MeasurableMul₂ G
μ ν : Measure G
inst✝³ : SigmaFinite ν
inst✝² : SigmaFinite μ
s : Set G
inst✝¹ : MeasurableInv G
inst✝ : IsMulLeftInvariant μ
hs : ↑↑μ s⁻¹ = 0
⊢ ↑↑μ s = 0
G : Type u_1
inst✝⁶ : MeasurableSpace G
inst✝⁵ : Group G
inst✝⁴ : MeasurableMul₂ G
μ ν : Measure G
inst✝³ : SigmaFinite ν
inst✝² : SigmaFinite μ
s : Set G
inst✝¹ : MeasurableInv G
inst✝ : IsMulLeftInvariant μ
⊢ ↑↑μ s⁻¹ = 0 ↔ ↑↑μ s = 0
refine' ⟨fun hs => _, (quasiMeasurePreserving_inv μ).preimage_null⟩
G : Type u_1
inst✝⁶ : MeasurableSpace G
inst✝⁵ : Group G
inst✝⁴ : MeasurableMul₂ G
μ ν : Measure G
inst✝³ : SigmaFinite ν
inst✝² : SigmaFinite μ
s : Set G
inst✝¹ : MeasurableInv G
inst✝ : IsMulLeftInvariant μ
hs : ↑↑μ s⁻¹ = 0
⊢ ↑↑μ s⁻¹⁻¹ = 0
G : Type u_1
inst✝⁶ : MeasurableSpace G
inst✝⁵ : Group G
inst✝⁴ : MeasurableMul₂ G
μ ν : Measure G
inst✝³ : SigmaFinite ν
inst✝² : SigmaFinite μ
s : Set G
inst✝¹ : MeasurableInv G
inst✝ : IsMulLeftInvariant μ
hs : ↑↑μ s⁻¹ = 0
⊢ ↑↑μ s = 0
rw [← inv_inv s]
no goals
G : Type u_1
inst✝⁶ : MeasurableSpace G
inst✝⁵ : Group G
inst✝⁴ : MeasurableMul₂ G
μ ν : Measure G
inst✝³ : SigmaFinite ν
inst✝² : SigmaFinite μ
s : Set G
inst✝¹ : MeasurableInv G
inst✝ : IsMulLeftInvariant μ
hs : ↑↑μ s⁻¹ = 0
⊢ ↑↑μ s⁻¹⁻¹ = 0
exact (quasiMeasurePreserving_inv μ).preimage_null hs