OAI/Analysis/LipschitzHilbert/Estimates/WeightedOrder.lean

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8 declarations, 0 contain sorry, 0 declared as axioms

Finite size-biased random orders

The recursive expectation below chooses the next element proportionally to its positive weight. This gives the same first-arrival probabilities as independent exponential clocks, while keeping the probability space entirely finite.

  1. def OAI.LipschitzHilbert.orderMass line 23
  2. def OAI.LipschitzHilbert.orderAverage line 25
  3. theorem OAI.LipschitzHilbert.orderAverage_empty line 33
  4. theorem OAI.LipschitzHilbert.orderAverage_nonempty line 38
  5. theorem OAI.LipschitzHilbert.orderMass_pos line 45
  6. theorem OAI.LipschitzHilbert.orderAverage_nonnegative line 49
  7. theorem OAI.LipschitzHilbert.orderAverage_const line 65
  8. theorem OAI.LipschitzHilbert.orderAverage_sum line 82