measurePreserving_hausdorffMeasure

English

An isometry equivalence preserves the Hausdorff measure for all d.

Русский

Изометрическое эквивалентное отображение сохраняет меру Хаусдорфа при любом d.

LaTeX

$$$\text{hausdorffMeasure } d$ is preserved by the isometry equivalence.$$

Lean4

theorem measurePreserving_hausdorffMeasure (e : X ≃ᵢ Y) (d : ℝ) : MeasurePreserving e μH[d] μH[d] :=
  ⟨e.continuous.measurable, map_hausdorffMeasure _ _⟩

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