OAI/NumberTheory/PrimePackets/ConditionalObservations.lean

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10 declarations, 0 contain sorry, 0 declared as axioms

Conditional entropy of finite observations

The conditioning variable is the last argument. All identities below use the actual distribution under μ, including its zero-mass cells.

  1. lemma OAI.PrimeDegreePackets.observationPair_measurable_fiber line 20
  2. def OAI.PrimeDegreePackets.conditionalObservationEntropy line 27
  3. lemma OAI.PrimeDegreePackets.observationEntropy_swap line 31
  4. lemma OAI.PrimeDegreePackets.observationEntropy_assoc line 37
  5. lemma OAI.PrimeDegreePackets.conditionalObservationEntropy_nonneg line 44
  6. lemma OAI.PrimeDegreePackets.conditionalObservationEntropy_le line 54
  7. lemma OAI.PrimeDegreePackets.conditionalObservationEntropy_chain line 63
  8. theorem OAI.PrimeDegreePackets.observationEntropy_submodular line 72
  9. theorem OAI.PrimeDegreePackets.conditionalObservationEntropy_conditioning_le line 107
  10. theorem OAI.PrimeDegreePackets.conditionalObservationEntropy_pair_le line 120