OAI/LinearAlgebra/MatrixMultiplication/Entropy/ComplexFiniteEntropy.lean

GitHub source file

17 declarations, 0 contain sorry, 0 declared as axioms

Finite entropy, rate estimates and ordered asymptotic limits.

  1. def OAI.MatrixMultiplication.Foundation.entropyTerm line 19
  2. def OAI.MatrixMultiplication.Foundation.finiteEntropy line 21
  3. theorem OAI.MatrixMultiplication.Foundation.finiteEntropy_equiv line 23
  4. theorem OAI.MatrixMultiplication.Foundation.entropyTerm_zero line 27
  5. theorem OAI.MatrixMultiplication.Foundation.entropyTerm_mul line 29
  6. theorem OAI.MatrixMultiplication.Foundation.finiteEntropy_chain line 39
  7. structure OAI.MatrixMultiplication.Foundation.FiniteLaw line 46
  8. def OAI.MatrixMultiplication.Foundation.FiniteLaw.map line 55
  9. theorem OAI.MatrixMultiplication.Foundation.FiniteLaw.map_mass line 67
  10. theorem OAI.MatrixMultiplication.Foundation.FiniteLaw.map_mass_apply line 75
  11. theorem OAI.MatrixMultiplication.Foundation.FiniteLaw.map_entropy_of_injective line 80
  12. def OAI.MatrixMultiplication.Foundation.FiniteLaw.joint line 95
  13. theorem OAI.MatrixMultiplication.Foundation.FiniteLaw.joint_entropy line 100
  14. theorem OAI.MatrixMultiplication.Foundation.FiniteLaw.mass_le_map_mass line 105
  15. def OAI.MatrixMultiplication.Foundation.FiniteLaw.conditional line 119
  16. theorem OAI.MatrixMultiplication.Foundation.FiniteLaw.map_mass_mul_conditional line 128
  17. theorem OAI.MatrixMultiplication.Foundation.FiniteLaw.entropy_eq_map_add_conditional line 148