OAI/NumberTheory/JointDickman/Amplification/SubsetThinning.lean

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4 declarations, 0 contain sorry, 0 declared as axioms

Fair thinning of an independently selected prime set

  1. def OAI.JointDickman.subsetRetentionMass line 13
  2. theorem OAI.JointDickman.fairRetentionMass_subsets line 16
  3. theorem OAI.JointDickman.subsetRetentionMass_marginal line 53
  4. theorem OAI.JointDickman.subsetRetentionMass_expectation line 71

    Source documentation

    Integrating both the first remaining set and its fair second coins leaves precisely the independent addition law with halved parameters.

    theorem subsetRetentionMass_expectation {α : Type*} [DecidableEq α]
    (P : Finset α) (q : α → ℝ) (F : Finset α → ℝ) :
    (∑ S ∈ P.powerset, bernoulliSubsetMass P q S *
      ∑ T ∈ P.powerset, subsetRetentionMass S T * F T) =
      ∑ T ∈ P.powerset, bernoulliSubsetMass P (fun p => q p / 2) T * F T := by
…

    Mentions: OAI.JointDickman.bernoulliSubsetMass, OAI.JointDickman.subsetRetentionMass