apply Filter.Eventually.mp hg_nonneg
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‖
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
⊢ ∀ᵐ (x : ℝ) ∂Measure.restrict μ s, 0 x ≤ g x → (fun x => g x) x = (fun a => ‖g a‖) x