diff --git a/Aristotle/Basic.lean b/Aristotle/Basic.lean index 0e1b0e8..331fcc7 100644 --- a/Aristotle/Basic.lean +++ b/Aristotle/Basic.lean @@ -1,8 +1,15 @@ import Mathlib -variable - {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E] -lemma MeromorphicAt.comp {x : ℝ} {f : ℂ → E} {g : ℝ → ℂ} - (hf : MeromorphicAt f (g x)) (hg : AnalyticAt ℝ g x) : MeromorphicAt (f ∘ g) x := by +theorem intervalIntegrable_iff_intervalIntegrable_smul + {E : Type*} [NormedAddCommGroup E] + {a b : ℝ} {μ : MeasureTheory.Measure ℝ} + {R : Type*} [NormedAddCommGroup R] [SMulZeroClass R E] [IsBoundedSMul R E] + {f : ℝ → E} {r : R} (hr : r ≠ 0) : + IntervalIntegrable f μ a b ↔ IntervalIntegrable (r • f) μ a b := by + sorry + +theorem IntervalIntegrable.abs' + {a b : ℝ} {μ : MeasureTheory.Measure ℝ} {f : ℝ → ℝ} (hf : Measurable f) : + IntervalIntegrable f μ a b ↔ IntervalIntegrable (fun x => |f x|) μ a b := by sorry