Theorems · Theorem · measure theory
MeasureTheory.AddContent.supClosure_apply_of_mem
∀ {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}, s ∈ C → (m.supClosure hC) s = m s- Defined in
- Mathlib.MeasureTheory.Measure.AddContent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddCommMonoidstatement and proof · cited by 12,281
- ClosureOperatorstatement · cited by 371
- MeasureTheory.IsSetSemiringstatement and proof · cited by 78
- MeasureTheory.AddContentstatement and proof · cited by 78
- supClosurestatement · cited by 33
- MeasureTheory.AddContent.supClosurestatement · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.addContent_le_sum_of_subset_sUnionproof · cited by 1