OAI/Geometry/RCD/Transport/RenyiPerturbation.lean

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6 declarations, 0 contain sorry, 0 declared as axioms

Quantitative increase of the concave power under mass replacement

The replacement used in the midpoint construction moves mass out of a superlevel set into a density bounded by the threshold. A strictly higher superlevel set supplies a positive gap.

  1. theorem OAI.RegularPointCoordinates.rpow_increment_lower line 17
  2. theorem OAI.RegularPointCoordinates.rpow_decrement_lower line 35
  3. theorem OAI.RegularPointCoordinates.renyiPerturb_low line 50
  4. theorem OAI.RegularPointCoordinates.renyiPerturb_high line 59
  5. def OAI.RegularPointCoordinates.renyiPerturbLower line 71
  6. theorem OAI.RegularPointCoordinates.renyiPerturb_power_lower line 75