Theorems · Theorem · measure theory
MeasureTheory.IsSetRing.biUnion_mem
∀ {α : Type u_1} {C : Set (Set α)} {ι : Type u_2},
MeasureTheory.IsSetRing C → ∀ {s : ι → Set α} (S : Finset ι), (∀ n ∈ S, s n ∈ C) → ⋃ i ∈ S, s i ∈ C- Defined in
- Mathlib.MeasureTheory.SetSemiring
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.coeproof · cited by 8,199
- Set.iUnionstatement and proof · cited by 2,483
- Set.iUnion_congr_Propproof · cited by 374
- Finset.mem_insert_selfproof · cited by 128
- Finset.coe_insertproof · cited by 124
- Finset.mem_insert_of_memproof · cited by 109
- Finset.inductionproof · cited by 108
- Set.iUnion_emptyproof · cited by 68
- Set.iUnion_of_emptyproof · cited by 68
- MeasureTheory.IsSetRingstatement and proof · cited by 32
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.addContent_biUnion_leproof · cited by 2
- MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetRingproof · cited by 2
- MeasureTheory.IsSetAlgebra.biUnion_memproof · cited by 2
- MeasureTheory.IsSetRing.finsetSup_memproof · cited by 1
- MeasureTheory.addContent_biUnion_eqproof · cited by 0