Update logpos.lean

Nevanlinna/logpos.lean

@@ -1,14 +1,14 @@
-import Mathlib.MeasureTheory.Integral.CircleIntegral
-import Nevanlinna.divisor
-import Nevanlinna.stronglyMeromorphicOn
-import Nevanlinna.meromorphicOn_divisor
+import Mathlib.Analysis.SpecialFunctions.Log.Basic
 
 open Real
 
 
 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
   rw [log_inv]
   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
 
 
-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
   · rw [norm_of_nonneg hr]
     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
     rw [this]
     ring
+
+-- WANT: logpos is even and continuous
+-- WANT: Inequalities