Theorems · Theorem · measure theory
subset_piiUnionInter
∀ {α : Type u_3} {ι : Type u_4} {π : ι → Set (Set α)} {S : Set ι} {i : ι}, i ∈ S → π i ⊆ piiUnionInter π S- Defined in
- Mathlib.MeasureTheory.PiSystem
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.Subset.transproof · cited by 218
- Set.mem_singleton_iffproof · cited by 172
- Set.subset_union_leftproof · cited by 142
- piiUnionInterstatement · cited by 20
- piiUnionInter_mono_rightproof · cited by 1
- piiUnionInter_singletonproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- mem_piiUnionInter_of_measurableSetproof · cited by 1
- le_generateFrom_piiUnionInterproof · cited by 1