Theorems · Theorem · measure theory
IsLowerSet.null_frontier
∀ {ι : Type u_1} [inst : Fintype ι] {s : Set (ι → ℝ)}, IsLowerSet s → MeasureTheory.volume (frontier s) = 0- Defined in
- Mathlib.MeasureTheory.Order.UpperLower
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 268 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.
Cites28
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
- Fintypestatement and proof · cited by 7,736
- Set.ofPredproof · cited by 6,101
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- nhdsWithinproof · cited by 1,912
- Set.Ioiproof · cited by 1,463
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
Cited by1
Results whose statement or proof uses this declaration.
- Set.OrdConnected.null_frontierproof · cited by 2