volume_preserving_ofLp — Mathlib

English

The canonical measurable equivalence between WithLp.ofLp and the Euclidean setting preserves volume.

Русский

Каноническое измеримое эквивалентное отображение между WithLp.ofLp и евклидовым сохраняет объём.

LaTeX

$$$\\text{WithLp.ofLp}$ preserves volume.$$

Lean4

/-- A copy of `EuclideanSpace.volume_preserving_measurableEquiv` for the canonical spelling of the
equivalence. -/
theorem volume_preserving_ofLp : MeasurePreserving (@WithLp.ofLp 2 (ι → ℝ)) :=
  EuclideanSpace.volume_preserving_measurableEquiv ι

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