Theorems · Inductive type · measure theory
MeasureTheory.IsSetRing
{α : Type u_1} → Set (Set α) → PropA ring of sets C is a family of sets containing ∅, stable by union and set difference.
It is then also stable by intersection (see IsSetRing.inter_mem).
- Defined in
- Mathlib.MeasureTheory.SetSemiring
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
Cited by35
Results whose statement or proof uses this declaration.
- MeasureTheory.IsSetRing.sdiff_memstatement and proof · cited by 9
- MeasureTheory.IsSetRing.isSetSemiringstatement and proof · cited by 6
- MeasureTheory.isSetRing_measurableCylindersstatement · cited by 6
- MeasureTheory.addContent_unionstatement and proof · cited by 6
- MeasureTheory.IsSetRing.union_memstatement and proof · cited by 5
- MeasureTheory.IsSetRing.biUnion_memstatement and proof · cited by 5
- MeasureTheory.IsSetRing.inter_memstatement and proof · cited by 5
- MeasureTheory.IsSetRing.accumulate_memstatement and proof · cited by 4
- MeasureTheory.IsSetSemiring.isSetRing_supClosurestatement · cited by 3
- MeasureTheory.addContent_accumulatestatement and proof · cited by 3
- MeasureTheory.addContent_sdiff_of_ne_topstatement and proof · cited by 3
- MeasureTheory.IsSetAlgebra.isSetRingstatement · cited by 3