@@ -349,7 +349,7 @@ theorem norm_integral_le_lintegral_norm (f : α → G) :
349349 · simp [integral, hG]
350350
351351theorem enorm_integral_le_lintegral_enorm (f : α → G) : ‖∫ a, f a ∂μ‖ₑ ≤ ∫⁻ a, ‖f a‖ₑ ∂μ := by
352- simp_rw [← ofReal_norm_eq_enorm ]
352+ simp_rw [← ofReal_norm ]
353353 apply ENNReal.ofReal_le_of_le_toReal
354354 exact norm_integral_le_lintegral_norm f
355355
@@ -536,7 +536,7 @@ theorem integral_eq_lintegral_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤ᵐ[μ] f
536536theorem integral_norm_eq_lintegral_enorm {P : Type *} [NormedAddCommGroup P] {f : α → P}
537537 (hf : AEStronglyMeasurable f μ) : ∫ x, ‖f x‖ ∂μ = (∫⁻ x, ‖f x‖ₑ ∂μ).toReal := by
538538 rw [integral_eq_lintegral_of_nonneg_ae _ hf.norm]
539- · simp_rw [ofReal_norm_eq_enorm ]
539+ · simp_rw [ofReal_norm ]
540540 · filter_upwards; simp_rw [Pi.zero_apply, norm_nonneg, imp_true_iff]
541541
542542theorem ofReal_integral_norm_eq_lintegral_enorm {P : Type *} [NormedAddCommGroup P] {f : α → P}
@@ -721,7 +721,7 @@ theorem ofReal_integral_eq_lintegral_ofReal {f : α → ℝ} (hfi : Integrable f
721721 ENNReal.ofReal (∫ x, f x ∂μ) = ∫⁻ x, ENNReal.ofReal (f x) ∂μ := by
722722 have : f =ᵐ[μ] (‖f ·‖) := f_nn.mono fun _x hx ↦ (abs_of_nonneg hx).symm
723723 simp_rw [integral_congr_ae this, ofReal_integral_norm_eq_lintegral_enorm hfi,
724- ← ofReal_norm_eq_enorm ]
724+ ← ofReal_norm ]
725725 exact lintegral_congr_ae (this.symm.fun_comp ENNReal.ofReal)
726726
727727theorem integral_toReal {f : α → ℝ≥0 ∞} (hfm : AEMeasurable f μ) (hf : ∀ᵐ x ∂μ, f x < ∞) :
@@ -939,7 +939,7 @@ theorem MemLp.eLpNorm_eq_integral_rpow_norm {f : α → H} {p : ℝ≥0∞} (hp1
939939 (hf : MemLp f p μ) :
940940 eLpNorm f p μ = ENNReal.ofReal ((∫ a, ‖f a‖ ^ p.toReal ∂μ) ^ p.toReal⁻¹) := by
941941 have A : ∫⁻ a : α, ENNReal.ofReal (‖f a‖ ^ p.toReal) ∂μ = ∫⁻ a : α, ‖f a‖ₑ ^ p.toReal ∂μ := by
942- simp_rw [← ofReal_rpow_of_nonneg (norm_nonneg _) toReal_nonneg, ofReal_norm_eq_enorm ]
942+ simp_rw [← ofReal_rpow_of_nonneg (norm_nonneg _) toReal_nonneg, ofReal_norm ]
943943 simp only [eLpNorm_eq_lintegral_rpow_enorm_toReal hp1 hp2, one_div]
944944 rw [integral_eq_lintegral_of_nonneg_ae]; rotate_left
945945 · exact ae_of_all _ fun x => by positivity
@@ -1205,13 +1205,13 @@ theorem integral_mul_norm_le_Lp_mul_Lq {E} [NormedAddCommGroup E] {f g : α →
12051205 -- replace norms by nnnorm
12061206 have h_left : ∫⁻ a, ENNReal.ofReal (‖f a‖ * ‖g a‖) ∂μ =
12071207 ∫⁻ a, ((‖f ·‖ₑ) * (‖g ·‖ₑ)) a ∂μ := by
1208- simp_rw [Pi.mul_apply, ← ofReal_norm_eq_enorm , ENNReal.ofReal_mul (norm_nonneg _)]
1208+ simp_rw [Pi.mul_apply, ← ofReal_norm , ENNReal.ofReal_mul (norm_nonneg _)]
12091209 have h_right_f : ∫⁻ a, .ofReal (‖f a‖ ^ p) ∂μ = ∫⁻ a, ‖f a‖ₑ ^ p ∂μ := by
12101210 refine lintegral_congr fun x => ?_
1211- rw [← ofReal_norm_eq_enorm , ENNReal.ofReal_rpow_of_nonneg (norm_nonneg _) hpq.nonneg]
1211+ rw [← ofReal_norm , ENNReal.ofReal_rpow_of_nonneg (norm_nonneg _) hpq.nonneg]
12121212 have h_right_g : ∫⁻ a, .ofReal (‖g a‖ ^ q) ∂μ = ∫⁻ a, ‖g a‖ₑ ^ q ∂μ := by
12131213 refine lintegral_congr fun x => ?_
1214- rw [← ofReal_norm_eq_enorm , ENNReal.ofReal_rpow_of_nonneg (norm_nonneg _) hpq.symm.nonneg]
1214+ rw [← ofReal_norm , ENNReal.ofReal_rpow_of_nonneg (norm_nonneg _) hpq.symm.nonneg]
12151215 rw [h_left, h_right_f, h_right_g]
12161216 -- we can now apply `ENNReal.lintegral_mul_le_Lp_mul_Lq` (up to the `toReal` application)
12171217 refine ENNReal.toReal_mono ?_ ?_
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