Theorems · Theorem · number theory
ZSpan.measure_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 (ZSpan.fundamentalDomain b) = ENNReal.ofReal |b₀.det ⇑b| * μ (ZSpan.fundamentalDomain b₀)- Defined in
- Mathlib.Algebra.Module.ZLattice.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
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
- Setstatement and proof · cited by 53,352
- 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
- ENNRealstatement and proof · cited by 9,879
- Equivproof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Set.preimageproof · cited by 4,946
- AddGroupproof · cited by 4,410
Cited by4
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasisproof · cited by 4
- ZSpan.measureReal_fundamentalDomainproof · cited by 1
- ZSpan.volume_fundamentalDomainproof · cited by 1