Theorems · Theorem · measure theory

Real.volume_preserving_transvectionStruct

∀ {ι : Type u_1} [inst : Fintype ι] [inst_1 : DecidableEq ι] (t : Matrix.TransvectionStruct ι ℝ),
  MeasureTheory.MeasurePreserving (⇑(Matrix.toLin' t.toMatrix)) MeasureTheory.volume MeasureTheory.volume

A transvection preserves Lebesgue measure.

Defined in: Mathlib.MeasureTheory.Measure.Lebesgue.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 243 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype DecidableEq

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setproof · cited by 53,352
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LinearMapstatement · cited by 10,215
ENNRealproof · cited by 9,879
Fintypestatement and proof · cited by 7,736
Matrixstatement · cited by 4,303
Set.univproof · cited by 3,945
Finset.univproof · cited by 3,473
LinearEquivstatement · cited by 3,317

Cited by1

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Real.map_matrix_volume_pi_eq_smul_volume_piproof · cited by 1