Theorems · Theorem · measure theory
MeasureTheory.Measure.addHaar_affineSubspace
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E] [BorelSpace E]
[FiniteDimensional ℝ E] (μ : MeasureTheory.Measure E) [μ.IsAddHaarMeasure] (s : AffineSubspace ℝ E), s ≠ ⊤ → μ ↑s = 0A strict affine subspace has measure zero.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Set.preimageproof · cited by 4,946
- Bot.botproof · cited by 4,720
Cited by4
Results whose statement or proof uses this declaration.
- ZSpan.fundamentalDomain_ae_parallelepipedproof · cited by 2
- NumberField.mixedEmbedding.realSpace.volume_eq_zeroproof · cited by 1
- Convex.addHaar_frontierproof · cited by 1
- NumberField.mixedEmbedding.volume_eq_zeroproof · cited by 1