OAI/MathematicalPhysics/Boltzmann/Compactness/KineticDensityMeasurable.lean

GitHub source file

14 declarations, 0 contain sorry, 0 declared as axioms

Measure-preserving grouping of physical time and phase coordinates

  1. def OAI.BoltzmannNonuniqueness.kineticDensity line 16
  2. theorem OAI.BoltzmannNonuniqueness.kineticGrouping_measurePreserving line 19
  3. theorem OAI.BoltzmannNonuniqueness.phaseInterval_measure line 26
  4. def OAI.BoltzmannNonuniqueness.KineticCollisionNullSets.left line 50
  5. def OAI.BoltzmannNonuniqueness.KineticCollisionNullSets.right line 53
  6. theorem OAI.BoltzmannNonuniqueness.KineticCollisionNullSets.left_quasiMeasurePreserving line 56
  7. theorem OAI.BoltzmannNonuniqueness.KineticCollisionNullSets.right_quasiMeasurePreserving line 68
  8. def OAI.BoltzmannNonuniqueness.KineticCollisionNullSets.gain line 80
  9. theorem OAI.BoltzmannNonuniqueness.KineticCollisionNullSets.gain_congr line 83
  10. theorem OAI.BoltzmannNonuniqueness.KineticCollisionNullSets.measurable_gain line 97
  11. def OAI.BoltzmannNonuniqueness.KineticCollisionNullSets.frequency line 117
  12. theorem OAI.BoltzmannNonuniqueness.KineticCollisionNullSets.frequency_congr line 120
  13. theorem OAI.BoltzmannNonuniqueness.KineticCollisionNullSets.measurable_frequency line 129
  14. theorem OAI.BoltzmannNonuniqueness.measurable_kineticDensity line 153