OAI/NumberTheory/Ostmann/Arithmetic/WeightedIntervalMass.lean

GitHub source file

5 declarations, 0 contain sorry, 0 declared as axioms

1. def OAI.Ostmann.weightedCDF line 11
2. def OAI.Ostmann.weightedIntervalMass line 14
3. theorem OAI.Ostmann.weightedCDF_mono line 17
4. theorem OAI.Ostmann.weightedCDF_sub line 27
5. theorem OAI.Ostmann.intervalNodeDensity_weightedCDF line 39

   Source documentation

   The concrete density on a tree node is its actual weighted interval mass divided by its interval length.

   theorem intervalNodeDensity_weightedCDF {M : ℕ} (hM : 0 < M)
       (P : Finset ℕ) (x μ : ℕ → ℝ) (a L : ℝ) (hL : 0 < L) (w : List (Fin M)) :
       intervalNodeDensity (weightedCDF P x μ) a L w =
         weightedIntervalMass P x μ (intervalNode a L w).1
           ((intervalNode a L w).1 + (intervalNode a L w).2) / (intervalNode a L w).2 := by
   …

   Mentions: OAI.Ostmann.intervalNodeDensity, OAI.Ostmann.weightedCDF, OAI.Ostmann.weightedIntervalMass, OAI.Ostmann.intervalNode