OAI/InformationTheory/Entanglement/MatrixFamilyDensity.lean

GitHub source file

13 declarations, 0 contain sorry, 0 declared as axioms

  1. def OAI.SecretKey.familyTraceMeasure line 14
  2. instance OAI.SecretKey.familyTraceMeasureIsFiniteMeasure line 16
  3. lemma OAI.SecretKey.trace_absolutelyContinuous_family line 20
  4. lemma OAI.SecretKey.familyTraceMeasure_real line 25
  5. def OAI.SecretKey.familyDensity line 30
  6. lemma OAI.SecretKey.familyDensity_psd line 32
  7. lemma OAI.SecretKey.familyDensity_measurable line 34
  8. lemma OAI.SecretKey.familyDensity_integrable line 36
  9. lemma OAI.SecretKey.familyDensity_trace_integrable line 39
  10. lemma OAI.SecretKey.familyDensity_setIntegral line 42
  11. lemma OAI.SecretKey.familyDensity_trace_setIntegral line 46
  12. theorem OAI.SecretKey.familyDensity_trace_sum_one line 52
  13. lemma OAI.SecretKey.familyDensity_total_integral line 62