OAI/MathematicalPhysics/ContinuumCoulomb/OneParticle/PlanarHeatLimit.lean

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6 declarations, 0 contain sorry, 0 declared as axioms

The Gaussian change of scale and the actual time-zero limit of the heat average. The bound by the normalized time-one Gaussian permits dominated convergence even though the Gaussian has noncompact support.

  1. theorem OAI.ContinuumCoulomb.planarHeatKernel_sqrt_scale line 16
  2. theorem OAI.ContinuumCoulomb.planarHeatAverage_scaled line 26
  3. theorem OAI.ContinuumCoulomb.planarScaledHeatIntegrand_measurable line 37
  4. theorem OAI.ContinuumCoulomb.planarScaledHeatIntegrand_bound line 44
  5. theorem OAI.ContinuumCoulomb.planarScaledHeatIntegrand_tendsto line 50
  6. theorem OAI.ContinuumCoulomb.planarHeatAverage_tendsto_zero line 62