Theorems · Theorem · measure theory
MeasurableSpace.measurableSet_generateFrom_countablePartition_iff
∀ {α : Type u_1} [m : MeasurableSpace α] [h : MeasurableSpace.CountablyGenerated α] (n : ℕ) (s : Set α),
MeasurableSet s ↔ ∃ S, ↑S ⊆ MeasurableSpace.countablePartition α n ∧ s = ⋃₀ ↑S- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 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
- Finsetstatement · cited by 13,712
- MeasurableSpacestatement and proof · cited by 13,106
- SetLike.coestatement · cited by 8,199
- MeasurableSetstatement · cited by 3,075
- Set.sUnionstatement · cited by 392
- MeasurableSpace.generateFromstatement · cited by 172
- MeasurableSpace.CountablyGeneratedstatement and proof · cited by 124
- MeasurableSpace.countablePartitionstatement · cited by 20
- Set.enumerateCountableproof · cited by 15
- MeasurableSpace.countable_countableGeneratingSetproof · cited by 13
- MeasurableSpace.measurableSet_generateFrom_memPartition_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.setIntegral_densityProcessproof · cited by 4