Theorems · Theorem · measure theory
MeasurableSpace.generateFrom_singleton
∀ {α : Type u_1} (s : Set α), MeasurableSpace.generateFrom {s} = MeasurableSpace.comap (fun x => x ∈ s) ⊤The sigma-algebra generated by a single set s is {∅, s, sᶜ, univ}.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- MeasurableSpacestatement and proof · cited by 13,106
- Top.topstatement · cited by 9,680
- Set.preimageproof · cited by 4,946
- MeasurableSetproof · cited by 3,075
- le_antisymmproof · cited by 2,068
- Set.mem_singletonproof · cited by 183
- MeasurableSpace.generateFromstatement and proof · cited by 172
- MeasurableSpace.comapstatement · cited by 124
- MeasurableSpace.generateFrom_leproof · cited by 49
- Set.preimage_singleton_trueproof · cited by 5
- MeasurableSet.memproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.measurableSet_generateFrom_singleton_iffproof · cited by 1
- ProbabilityTheory.Kernel.indepSet_zero_rightproof · cited by 0
- ProbabilityTheory.Kernel.iIndepSet_zero_rightproof · cited by 0
- ProbabilityTheory.Kernel.indepSet_zero_leftproof · cited by 0