Theorems · Theorem · measure theory
MeasureTheory.IsSetSemiring.pairwiseDisjoint_union_disjointOfDiffUnion
∀ {α : Type u_1} {C : Set (Set α)} {s : Set α} {I : Finset (Set α)} (hC : MeasureTheory.IsSetSemiring C) (hs : s ∈ C)
(hI : ↑I ⊆ C), (↑I).PairwiseDisjoint id → (↑I ∪ ↑(hC.disjointOfDiffUnion hs hI)).PairwiseDisjoint id- Defined in
- Mathlib.MeasureTheory.SetSemiring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.PairwiseDisjointstatement and proof · cited by 275
- MeasureTheory.IsSetSemiringstatement and proof · cited by 78
- Set.subset_sUnion_of_memproof · cited by 39
- MeasureTheory.IsSetSemiring.disjointOfDiffUnionstatement and proof · cited by 16
- Set.disjoint_of_subsetproof · cited by 7
- MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiffUnionproof · cited by 2
- MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiffUnionproof · cited by 2
- Set.pairwiseDisjoint_unionproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.addContent_eq_add_disjointOfDiffUnion_of_subsetproof · cited by 1