Theorems · Definition · measure theory
MeasurableSpace.countablyGeneratedAtom
(α : Type u_3) → [inst : MeasurableSpace α] → [MeasurableSpace.CountablyGenerated α] → (ℕ → Prop) → Set α
The atoms in a countably generated measurable space.
Some of those sets may be empty, but the nonempty ones are the atoms of the measurable space.
See measurableAtom_eq_countablyGeneratedAtom_natGeneratingSequence.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- Compl.complproof · cited by 2,925
- Set.iInterproof · cited by 1,084
- MeasurableSpace.CountablyGeneratedstatement and proof · cited by 124
- MeasurableSpace.natGeneratingSequenceproof · cited by 11
Cited by7
Results whose statement or proof uses this declaration.
- MeasurableSpace.mem_countablyGeneratedAtom_natGeneratingSequencestatement · cited by 2
- MeasurableSpace.measurableSet_countablyGeneratedAtomstatement · cited by 2
- MeasurableSpace.disjoint_countablyGeneratedAtomstatement and proof · cited by 2
- MeasurableSpace.measurableAtom_eq_countablyGeneratedAtom_natGeneratingSequencestatement and proof · cited by 1
- MeasurableSpace.exists_eq_iUnion_countablyGeneratedAtomstatement and proof · cited by 1
- MeasurableSpace.countablyGeneratedAtom.congr_simpstatement and proof · cited by 0
- MeasurableSpace.iUnion_countablyGeneratedAtomstatement · cited by 0