Theorems · Definition · measure theory
MeasurableSpace.countablePartition
(α : Type u_3) → [inst : MeasurableSpace α] → [MeasurableSpace.CountablyGenerated α] → ℕ → Set (Set α)
For each n : ℕ, countablePartition α n is a partition of the space in at most
2^n sets. Each partition is finer than the preceding one. The measurable space generated by
the union of all those partitions is the measurable space on α.
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 81 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
- MeasurableSpace.CountablyGeneratedstatement and proof · cited by 124
- memPartitionproof · cited by 20
- Set.enumerateCountableproof · cited by 15
- MeasurableSpace.countable_countableGeneratingSetproof · cited by 13
Cited by21
Results whose statement or proof uses this declaration.
- ProbabilityTheory.countableFiltrationproof · cited by 23
- MeasurableSpace.measurableSet_countablePartitionstatement and proof · cited by 5
- ProbabilityTheory.Kernel.setIntegral_densityProcessproof · cited by 4
- MeasurableSpace.countablePartitionSet_memstatement · cited by 4
- ProbabilityTheory.measurable_countablePartitionSet_subtypestatement and proof · cited by 2
- ProbabilityTheory.Kernel.densityProcess_fst_univ_aeproof · cited by 2
- MeasurableSpace.disjoint_countablePartitionstatement and proof · cited by 2
- MeasurableSpace.generateFrom_iUnion_countablePartitionstatement · cited by 1
- ProbabilityTheory.measurableSet_countableFiltration_of_memstatement and proof · cited by 1
- ProbabilityTheory.iSup_countableFiltrationproof · cited by 1
- MeasurableSpace.measurableSet_generateFrom_countablePartition_iffstatement · cited by 1