OAI/Analysis/CircleDomains/Sobolev/MaximalTruncations.lean

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11 declarations, 0 contain sorry, 0 declared as axioms

Bounded compactly supported increasing approximations to a nonnegative L² function. Each fixed ball integral converges to the original integral.

  1. def OAI.CircleDomainRigidity.maximalInputTruncation line 14
  2. lemma OAI.CircleDomainRigidity.measurable_maximalInputTruncation line 17
  3. lemma OAI.CircleDomainRigidity.maximalInputTruncation_nonneg line 21
  4. lemma OAI.CircleDomainRigidity.maximalInputTruncation_le line 25
  5. lemma OAI.CircleDomainRigidity.maximalInputTruncation_le_bound line 31
  6. lemma OAI.CircleDomainRigidity.maximalInputTruncation_mono line 37
  7. lemma OAI.CircleDomainRigidity.maximalInputTruncation_eventually_eq line 47
  8. lemma OAI.CircleDomainRigidity.maximalInputTruncation_memLp line 57
  9. lemma OAI.CircleDomainRigidity.maximalInputTruncation_integrable line 65
  10. lemma OAI.CircleDomainRigidity.maximalInputTruncation_energy_le line 82
  11. lemma OAI.CircleDomainRigidity.tendsto_integral_maximalInputTruncation line 90