OAI/Geometry/RCD/Sobolev/SobolevWeakEnergyLower.lean

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Weak Sobolev convergence and positive weighted energy bounds

Strong L2 convergence and a bounded Sobolev norm suffice. No compactness or convergence of the gradients is assumed.

  1. theorem OAI.RegularPointCoordinates.bounded_sobolev_functional_tendsto line 20
  2. theorem OAI.RegularPointCoordinates.weightedGamma_nonneg_of_weight line 33
  3. theorem OAI.RegularPointCoordinates.weighted_energy_lower_eventually line 40
  4. theorem OAI.RegularPointCoordinates.weighted_energy_le_of_bounded_L2_limit line 64