rw [integral_congr_ae]
case hz'
f g : ℝ → ℝ
s : Set ℝ
μ : Measure ℝ
hs_ne : Set.Nonempty s
hs_meas : MeasurableSet s
hs_conn : IsPreconnected s
hs_closed : IsClosed s
hf_cont : ContinuousOn f s
hg_int : IntegrableOn g s
hg_nonneg : 0 ≤ᵐ[Measure.restrict μ s] g
h_int : IntegrableOn (fun x => f x * g x) s
⊢ ∫ (x : ℝ) in s, g x ∂μ = ∫ (x : ℝ) in s, ‖g x‖ ∂μ
case hz'
f g : ℝ → ℝ
s : Set ℝ
μ : Measure ℝ
hs_ne : Set.Nonempty s
hs_meas : MeasurableSet s
hs_conn : IsPreconnected s
hs_closed : IsClosed s
hf_cont : ContinuousOn f s
hg_int : IntegrableOn g s
hg_nonneg : 0 ≤ᵐ[Measure.restrict μ s] g
h_int : IntegrableOn (fun x => f x * g x) s
⊢ (fun x => g x) =ᵐ[Measure.restrict μ s] fun a => ‖g a‖