Theorems · Theorem · measure theory

MeasureTheory.AddContent.supClosure_apply

∀ {α : Type u_1} {C : Set (Set α)} {G : Type u_2} [inst : AddCommMonoid G] (hC : MeasureTheory.IsSetSemiring C)
  (m : MeasureTheory.AddContent G C) {s : Set α} {J : Finset (Set α)},
  ↑J ⊆ C → (↑J).PairwiseDisjoint id → s = ⋃₀ ↑J → (m.supClosure hC) s = ∑ s ∈ J, m s

Defined in: Mathlib.MeasureTheory.Measure.AddContent
Cited by: 1 results in Mathlib
Foundations: Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddCommMonoid

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Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
Setstatement and proof · cited by 53,352
Finsetstatement and proof · cited by 13,712
AddCommMonoidstatement and proof · cited by 12,281
SetLike.coestatement and proof · cited by 8,199
Finset.sumstatement · cited by 5,195
Set.sUnionstatement and proof · cited by 392
ClosureOperatorstatement · cited by 371
Set.PairwiseDisjointstatement and proof · cited by 275
MeasureTheory.IsSetSemiringstatement and proof · cited by 78
MeasureTheory.AddContentstatement and proof · cited by 78
supClosurestatement · cited by 33

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.AddContent.supClosure_apply_finpartitionproof · cited by 1