Theorems · Theorem · measure theory
MeasureTheory.hausdorffMeasure_pi_real
∀ {ι : Type u_4} [inst : Fintype ι], MeasureTheory.Measure.hausdorffMeasure ↑(Fintype.card ι) = MeasureTheory.volumeIn the space ι → ℝ, the Hausdorff measure coincides exactly with the Lebesgue measure.
- Defined in
- Mathlib.MeasureTheory.Measure.Hausdorff
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 249 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites95
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealproof · cited by 9,879
- Top.topproof · cited by 9,680
- Fintypestatement and proof · cited by 7,736
- nhdsproof · cited by 5,554
- Set.univproof · cited by 3,945
- mul_oneproof · cited by 3,885
- Filter.Tendstoproof · cited by 3,814
- Finset.univproof · cited by 3,473
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.hausdorffMeasure_realproof · cited by 2
- Real.dimH_ball_piproof · cited by 2
- MeasureTheory.hausdorffMeasure_prod_realproof · cited by 0