Theorems · Theorem · number theory

ZSpan.measureReal_fundamentalDomain

∀ {E : Type u_1} {ι : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] (b : Module.Basis ι ℝ E)
  [inst_2 : Fintype ι] [inst_3 : DecidableEq ι] [inst_4 : MeasurableSpace E] (μ : MeasureTheory.Measure E)
  [BorelSpace E] [μ.IsAddHaarMeasure] (b₀ : Module.Basis ι ℝ E),
  μ.real (ZSpan.fundamentalDomain b) = |b₀.det ⇑b| * μ.real (ZSpan.fundamentalDomain b₀)

Defined in: Mathlib.Algebra.Module.ZLattice.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace Fintype DecidableEq MeasurableSpace BorelSpace MeasureTheory.Measure.IsAddHaarMeasure

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Cites19

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
Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
NormedSpacestatement and proof · cited by 12,499
MeasureTheory.Measurestatement and proof · cited by 10,939
Fintypestatement and proof · cited by 7,736
absstatement and proof · cited by 1,814
BorelSpacestatement and proof · cited by 1,602
Module.Basisstatement and proof · cited by 1,477
ENNReal.toRealproof · cited by 859
MeasureTheory.Measure.realstatement · cited by 530

Cited by1

Results whose statement or proof uses this declaration.

ZLattice.covolume_eq_det_mul_measureRealproof · cited by 0