diff --git a/Mathlib/Analysis/SpecialFunctions/JapaneseBracket.lean b/Mathlib/Analysis/SpecialFunctions/JapaneseBracket.lean index c3a00d8725ab3..219d637a94e56 100644 --- a/Mathlib/Analysis/SpecialFunctions/JapaneseBracket.lean +++ b/Mathlib/Analysis/SpecialFunctions/JapaneseBracket.lean @@ -141,8 +141,7 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E] theorem integrable_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) : Integrable fun x : E => (1 + ‖x‖) ^ (-r) := by constructor - · -- porting note: was `measurability` - exact ((measurable_norm.const_add _).pow_const _).aestronglyMeasurable + · measurability -- Lower Lebesgue integral have : (∫⁻ a : E, ‖(1 + ‖a‖) ^ (-r)‖₊) = ∫⁻ a : E, ENNReal.ofReal ((1 + ‖a‖) ^ (-r)) := lintegral_nnnorm_eq_of_nonneg fun _ => rpow_nonneg (by positivity) _ @@ -156,8 +155,7 @@ theorem integrable_rpow_neg_one_add_norm_sq [MeasureSpace E] [BorelSpace E] have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr refine ((integrable_one_add_norm hnr).const_mul <| (2 : ℝ) ^ (r / 2)).mono' ?_ (eventually_of_forall fun x => ?_) - · -- porting note: was `measurability` - exact (((measurable_id.norm.pow_const _).const_add _).pow_const _).aestronglyMeasurable + · measurability refine (abs_of_pos ?_).trans_le (rpow_neg_one_add_norm_sq_le x hr) positivity #align integrable_rpow_neg_one_add_norm_sq integrable_rpow_neg_one_add_norm_sq