OAI/Analysis/FreeEntropy/GaussianConvolution.lean

GitHub source file

15 declarations, 0 contain sorry, 0 declared as axioms

  1. def OAI.FiniteEntropySeparation.smoothedDensity line 12
  2. def OAI.FiniteEntropySeparation.smoothedTimeDerivative line 14
  3. def OAI.FiniteEntropySeparation.smoothedGradient line 16
  4. def OAI.FiniteEntropySeparation.smoothedSecond line 18
  5. theorem OAI.FiniteEntropySeparation.normalKernel_le line 20
  6. theorem OAI.FiniteEntropySeparation.normalKernel_integrable_finite line 24
  7. theorem OAI.FiniteEntropySeparation.smoothedDensity_pos line 29
  8. theorem OAI.FiniteEntropySeparation.smoothedDensity_continuous line 35
  9. theorem OAI.FiniteEntropySeparation.normalKernel_product_integrable line 42
  10. theorem OAI.FiniteEntropySeparation.smoothedDensity_integrable line 48
  11. theorem OAI.FiniteEntropySeparation.smoothedDensity_integral line 51
  12. theorem OAI.FiniteEntropySeparation.smoothedDensity_hasDeriv_time line 56
  13. theorem OAI.FiniteEntropySeparation.smoothedDensity_hasDeriv_coordinate line 70
  14. theorem OAI.FiniteEntropySeparation.smoothedGradient_hasDeriv_coordinate line 82
  15. theorem OAI.FiniteEntropySeparation.smoothed_heatEquation line 94