Theorems · Theorem · number theory
NumberField.mixedEmbedding.realSpace.volume_eq_zero
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (w : NumberField.InfinitePlace K),
MeasureTheory.volume {x | x w = 0} = 0The set of points in the realSpace that are equal to 0 at a fixed place has volume zero.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 243 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Set.ofPredstatement and proof · cited by 6,101
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integralproof · cited by 2