volume_preserving_mixedSpaceToRealMixedSpace_symm

English

The symmetry of polar coordinates preserves volume in the mixed embedding setting.

Русский

Симметрия полярных координат сохраняет объем в смешанном вложении.

LaTeX

$$$\\text{volumePreserving}(\\text{PolarCoordRealSymm})(K)$$$

Lean4

theorem volume_preserving_mixedSpaceToRealMixedSpace_symm : MeasurePreserving (mixedSpaceToRealMixedSpace K).symm :=
  (MeasurePreserving.id _).prod <| volume_preserving_pi fun _ ↦ Complex.volume_preserving_equiv_real_prod.symm

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