OAI/Analysis/CircleDomains/Modulus/CostSummands.lean

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9 declarations, 0 contain sorry, 0 declared as axioms

The three disjoint cost summands can be recovered from the total measure. In particular a total barycenter density gives the physical occupation density on the original domain.

  1. theorem OAI.CircleDomainRigidity.measurableEmbedding_costPhysical line 20
  2. theorem OAI.CircleDomainRigidity.measurableEmbedding_costAtomic line 26
  3. theorem OAI.CircleDomainRigidity.measurableEmbedding_costTuple line 33
  4. def OAI.CircleDomainRigidity.sumCostMeasures line 39
  5. theorem OAI.CircleDomainRigidity.lintegral_sumCostMeasures line 43
  6. theorem OAI.CircleDomainRigidity.sumCostMeasures_physical line 52
  7. theorem OAI.CircleDomainRigidity.sumCostMeasures_atomic line 75
  8. theorem OAI.CircleDomainRigidity.sumCostMeasures_tuple line 98
  9. theorem OAI.CircleDomainRigidity.sumCostMeasures_absolutelyContinuous line 121