OAI/Analysis/KadisonKastler/StateActionStates.lean

GitHub source file

3 declarations, 0 contain sorry, 0 declared as axioms

States composed with probability averages

Positivity is proved on vectors, so the initial state need not be normal.

  1. theorem OAI.KadisonKastler.probabilityOperatorIntegral_positive line 21
  2. theorem OAI.KadisonKastler.stateActionAverage_square_positive line 45
  3. theorem OAI.KadisonKastler.state_comp_actionAverage line 60