Theorems · Theorem · measure theory
Set.OrdConnected.null_frontier
∀ {ι : Type u_1} [inst : Fintype ι] {s : Set (ι → ℝ)}, s.OrdConnected → MeasureTheory.volume (frontier s) = 0- Defined in
- Mathlib.MeasureTheory.Order.UpperLower
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 269 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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 · cited by 10,939
- ENNRealstatement · cited by 9,879
- SetLike.coeproof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- closureproof · cited by 1,254
- frontierstatement and proof · cited by 214
- Set.OrdConnectedstatement and proof · cited by 161
- upperClosureproof · cited by 84
Cited by2
Results whose statement or proof uses this declaration.
- Set.OrdConnected.nullMeasurableSetproof · cited by 0
- IsAntichain.volume_eq_zeroproof · cited by 0