Theorems · Theorem · measure theory
MeasureTheory.IsSetSemiring.disjointOfUnion_props
∀ {α : Type u_1} {C : Set (Set α)} {J : Finset (Set α)},
MeasureTheory.IsSetSemiring C →
↑J ⊆ C →
∃ K,
(↑J).PairwiseDisjoint K ∧
(∀ i ∈ J, ↑(K i) ⊆ C) ∧
(⋃ x ∈ J, ↑(K x)).PairwiseDisjoint id ∧
(∀ j ∈ J, ⋃₀ ↑(K j) ⊆ j) ∧ (∀ j ∈ J, ∅ ∉ K j) ∧ ⋃₀ ↑J = ⋃₀ ⋃ x ∈ J, ↑(K x)- Defined in
- Mathlib.MeasureTheory.SetSemiring
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
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.iUnionstatement · cited by 2,483
- Set.sUnionstatement · cited by 392
- Set.PairwiseDisjointstatement · cited by 275
- MeasureTheory.IsSetSemiringstatement and proof · cited by 78
- MeasureTheory.IsSetSemiring.disjointOfUnionproof · cited by 10
- MeasureTheory.IsSetSemiring.disjointOfUnion_subset_of_memproof · cited by 2
- MeasureTheory.IsSetSemiring.disjointOfUnion_subsetproof · cited by 1
- MeasureTheory.IsSetSemiring.empty_notMem_disjointOfUnionproof · cited by 1
- MeasureTheory.IsSetSemiring.pairwiseDisjoint_biUnion_disjointOfUnionproof · cited by 1
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