apply integral_eq_zero_of_ae
case inl
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
z : NNReal
hz : ENNReal.toNNReal (∫⁻ (x : ℝ) in s, ↑‖g x‖₊ ∂μ) = z
hz_zero : z = 0
hz' : ∫ (x : ℝ) in s, g x ∂μ = 0
⊢ ∫ (x : ℝ) in s, f x * g x ∂μ = 0
case inl.hf
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
z : NNReal
hz : ENNReal.toNNReal (∫⁻ (x : ℝ) in s, ↑‖g x‖₊ ∂μ) = z
hz_zero : z = 0
hz' : ∫ (x : ℝ) in s, g x ∂μ = 0
⊢ (fun a => f a * g a) =ᵐ[Measure.restrict μ s] 0