OAI/GroupTheory/PolycyclicRecognition/Algebra/GroupAveragedRepresentative.lean

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Exactly invariant representatives from group averaging

A probability equivalent to Haar measure is quasi-preserved by every right translation. On the invariant measurable set where an orbit function is essentially constant, its group integral is that constant. Assigning zero on the complement gives a measurable, everywhere invariant representative.

  1. def OAI.PolycyclicRecognition.groupAverage line 24
  2. def OAI.PolycyclicRecognition.groupAverageGood line 26
  3. theorem OAI.PolycyclicRecognition.measurable_groupAverage line 29
  4. theorem OAI.PolycyclicRecognition.measurableSet_groupAverageGood line 34
  5. theorem OAI.PolycyclicRecognition.groupAverageGood_smul line 50
  6. theorem OAI.PolycyclicRecognition.measurable_invariantRepresentative_of_groupAverage line 61