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Update logpos.lean

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This commit is contained in:
Stefan Kebekus 2024-12-20 15:27:06 +01:00
parent 0139e9c95a
commit c218c59225
1 changed files with 9 additions and 6 deletions
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Nevanlinna/logpos.lean
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@ -1,14 +1,14 @@
import Mathlib.MeasureTheory.Integral.CircleIntegral import Mathlib.Analysis.SpecialFunctions.Log.Basic
import Nevanlinna.divisor
import Nevanlinna.stronglyMeromorphicOn
import Nevanlinna.meromorphicOn_divisor
open Real open Real
noncomputable def logpos : ℝ → ℝ := fun r ↦ max 0 (log r) noncomputable def logpos : ℝ → ℝ := fun r ↦ max 0 (log r)
theorem loglogpos {r : ℝ} : log r = logpos r - logpos r⁻¹ := by notation "log⁺" => logpos
theorem loglogpos {r : ℝ} : log r = log⁺ r - log⁺ r⁻¹ := by
unfold logpos unfold logpos
rw [log_inv] rw [log_inv]
by_cases h : 0 ≤ log r by_cases h : 0 ≤ log r
@ -19,7 +19,7 @@ theorem loglogpos {r : ℝ} : log r = logpos r - logpos r⁻¹ := by
exact neg_nonneg.mp this exact neg_nonneg.mp this
theorem logpos_norm {r : ℝ} : logpos r = 2⁻¹ * (log r + ‖log r‖) := by theorem logpos_norm {r : ℝ} : log⁺ r = 2⁻¹ * (log r + ‖log r‖) := by
by_cases hr : 0 ≤ log r by_cases hr : 0 ≤ log r
· rw [norm_of_nonneg hr] · rw [norm_of_nonneg hr]
have : logpos r = log r := by have : logpos r = log r := by
@ -34,3 +34,6 @@ theorem logpos_norm {r : ℝ} : logpos r = 2⁻¹ * (log r + ‖log r‖) := by
exact le_of_not_ge hr exact le_of_not_ge hr
rw [this] rw [this]
ring ring
-- WANT: logpos is even and continuous
-- WANT: Inequalities