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feat(MeasureTheory): prove the TFAE characterizations of Jordan measurability - #666

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teorth:mainfrom
Chessing234:measure-jordan-equiv
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feat(MeasureTheory): prove the TFAE characterizations of Jordan measurability#666
Chessing234 wants to merge 3 commits into
teorth:mainfrom
Chessing234:measure-jordan-equiv

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Summary

  • Exercise 1.1.5: a bounded set is Jordan measurable iff it has an elementary sandwich of arbitrarily small measure iff it is within arbitrarily small outer measure of an elementary set.
  • Boolean closure already calls JordanMeasurable.equiv.out 0 1, so filling this sorry also completes those proofs.
  • The theorem is placed after IsElementary.isBounded so the 3→1 direction can use that.

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…rability
Exercise 1.1.5: inner=outer iff elementary sandwich iff small outer
symmetric difference. Boolean closure already uses this TFAE, so filling
it removes a sorry from those proofs.
Set.symmDiff_subset_union is a membership lemma here, not a subset, so
the 3→1 direction of the TFAE failed to typecheck.
simp already closed the identity, so tauto had nothing left to do.
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