[Merged by Bors] - feat(measure_theory/measure/hausdorff): (μH[1] : measure ℝ) = volume
#18982
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| theorem hausdorff_measure_measure_preserving_fun_unique [unique ι] | ||
| [topological_space.second_countable_topology X] (d : ℝ) : | ||
| measure_preserving (measurable_equiv.fun_unique ι X) μH[d] μH[d] := |
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Do we have this for any isometry_equiv?
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I think it's only true for isometry equivs which are also measurable
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Ah nevermind, my comment was stupid. Updated.
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Otherwise LGTM. Thanks! |
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Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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#18982) And similarly for `(μH[2] : measure ℝ × ℝ) = volume`. This addresses the TODO comment in the docstring. The `hausdorff_measure_pi_real` proof has been moved to the bottom of the file so that it can be kept next to the new results.
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(μH[1] : measure ℝ) = volume(μH[1] : measure ℝ) = volume
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* leanprover-community/mathlib#19025 (already changed while porting) * leanprover-community/mathlib#18982
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And similarly for
(μH[2] : measure ℝ × ℝ) = volume.This addresses the TODO comment in the docstring.
The
hausdorff_measure_pi_realproof has been moved to the bottom of the file so that it can be kept next to the new results.