Theorems · Theorem · number theory
ZLattice.covolume_eq_measure_fundamentalDomain
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E]
[inst_3 : MeasurableSpace E] [BorelSpace E] (L : Submodule ℤ E) [inst_5 : DiscreteTopology ↥L] [IsZLattice ℝ L]
(μ : autoParam (MeasureTheory.Measure E) _auto_19✝) [μ.IsAddHaarMeasure] {F : Set E},
MeasureTheory.IsAddFundamentalDomain (↥L) F μ → ZLattice.covolume L μ = μ.real F- Defined in
- Mathlib.Algebra.Module.ZLattice.Covolume
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Submodulestatement and proof · cited by 7,192
- FiniteDimensionalstatement and proof · cited by 1,854
- BorelSpacestatement and proof · cited by 1,602
- ENNReal.toRealproof · cited by 859
- MeasureTheory.Measure.realstatement · cited by 530
- DiscreteTopologystatement and proof · cited by 373
Cited by6
Results whose statement or proof uses this declaration.
- ZLattice.covolume_comapproof · cited by 3
- ZLattice.covolume_eq_detproof · cited by 3
- NumberField.mixedEmbedding.covolume_idealLatticeproof · cited by 1
- ZLattice.covolume_ne_zeroproof · cited by 1
- NumberField.mixedEmbedding.covolume_integerLatticeproof · cited by 0
- ZLattice.covolume_eq_det_mul_measureRealproof · cited by 0