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docs(Measure/Haar/OfBasis): expand a docstring (#17270)
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urkud committed Oct 2, 2024
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13 changes: 12 additions & 1 deletion Mathlib/MeasureTheory/Measure/Haar/OfBasis.lean
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Expand Up @@ -290,7 +290,18 @@ end Fintype
/-- A finite dimensional inner product space has a canonical measure, the Lebesgue measure giving
volume `1` to the parallelepiped spanned by any orthonormal basis. We define the measure using
some arbitrary choice of orthonormal basis. The fact that it works with any orthonormal basis
is proved in `orthonormalBasis.volume_parallelepiped`. -/
is proved in `orthonormalBasis.volume_parallelepiped`.
This instance creates:
- a potential non-defeq diamond with the natural instance for `MeasureSpace (ULift E)`,
which does not exist in Mathlib at the moment;
- a diamond with the existing instance `MeasureTheory.Measure.instMeasureSpacePUnit`.
However, we've decided not to refactor until one of these diamonds starts creating issues, see
https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Hausdorff.20measure.20normalisation
-/
instance (priority := 100) measureSpaceOfInnerProductSpace [NormedAddCommGroup E]
[InnerProductSpace ℝ E] [FiniteDimensional ℝ E] [MeasurableSpace E] [BorelSpace E] :
MeasureSpace E where volume := (stdOrthonormalBasis ℝ E).toBasis.addHaar
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