Theorem: integrable_Lp_mul_Lq (ForML/LpHoelder.lean)

State before:
E : Type u_1
inst✝¹ : MeasurableSpace E
μ : Measure E
p q : ℝ≥0∞
hpq : p⁻¹ + q⁻¹ = 1
𝕜 : Type u_2
inst✝ : NormedRing 𝕜
f : E → 𝕜
hf : Memℒp f p
g : E → 𝕜
hg : Memℒp g q
⊢ Integrable (f * g)
Tactic:
rw [← memℒp_one_iff_integrable]
State after:
E : Type u_1
inst✝¹ : MeasurableSpace E
μ : Measure E
p q : ℝ≥0∞
hpq : p⁻¹ + q⁻¹ = 1
𝕜 : Type u_2
inst✝ : NormedRing 𝕜
f : E → 𝕜
hf : Memℒp f p
g : E → 𝕜
hg : Memℒp g q
⊢ Memℒp (f * g) 1

State before:
E : Type u_1
inst✝¹ : MeasurableSpace E
μ : Measure E
p q : ℝ≥0∞
hpq : p⁻¹ + q⁻¹ = 1
𝕜 : Type u_2
inst✝ : NormedRing 𝕜
f : E → 𝕜
hf : Memℒp f p
g : E → 𝕜
hg : Memℒp g q
⊢ Memℒp (f * g) 1
Tactic:
exact memL1_Lp_mul_Lq hpq hf hg
State after:
no goals