OAI/NumberTheory/Ostmann/Construction/PrimeSubsetCellMixture.lean

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Exact cell reconstruction of the original harmonic prime law

  1. theorem OAI.Ostmann.primeSubsetLogMeasure_cells line 12
  2. theorem OAI.Ostmann.BulkIntegrand.average_originalPrimeCells line 25

    Source documentation

    The original normalized subset prior equals the mixture of its complete log/residue cells, with the same single normalization constant.

    theorem BulkIntegrand.average_originalPrimeCells {σ C : Type*} [Fintype σ] [Fintype C]
        (f : BulkIntegrand σ) (P : Finset ℕ) (q : ℕ) (a : C → ℕ) (u v : C → ℝ)
        (hSP : primeCellSupport q a u v ⊆ P)
        (hsep : ∀ c d, c ≠ d → ¬Nat.ModEq q (a c) (a d) ∨ v c ≤ u d ∨ v d ≤ u c)
        (i : σ) (x : σ → ℝ) :
        let S := primeCellSupport q a u v
    …

    Mentions: OAI.Ostmann.BulkIntegrand, OAI.Ostmann.primeCellSupport