Theorems · Definition · probability
ProbabilityTheory.countableFiltration
(α : Type u_2) → [m : MeasurableSpace α] → [MeasurableSpace.CountablyGenerated α] → MeasureTheory.Filtration ℕ m
A filtration built from the measurable spaces generated by countablePartition α n for
all n : ℕ.
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 86 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.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Filtrationstatement · cited by 425
- MeasurableSpace.generateFromproof · cited by 172
- MeasurableSpace.CountablyGeneratedstatement and proof · cited by 124
- MeasurableSpace.countablePartitionproof · cited by 20
- MeasurableSpace.generateFrom_countablePartition_leproof · cited by 1
Cited by23
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.setIntegral_densityProcessstatement · cited by 4
- ProbabilityTheory.Kernel.martingale_densityProcessstatement · cited by 3
- ProbabilityTheory.Kernel.setIntegral_densityProcess_of_lestatement and proof · cited by 2
- ProbabilityTheory.Kernel.setIntegral_density_of_measurableSetstatement · cited by 2
- ProbabilityTheory.measurable_countablePartitionSet_subtypestatement · cited by 2
- ProbabilityTheory.Kernel.setIntegral_densityproof · cited by 2
- ProbabilityTheory.Kernel.tendsto_densityProcess_limitProcessstatement · cited by 2
- ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcessstatement · cited by 2
- ProbabilityTheory.Kernel.density_ae_eq_limitProcessstatement and proof · cited by 2
- ProbabilityTheory.Kernel.measurable_densityProcess_auxproof · cited by 2
- ProbabilityTheory.Kernel.measurable_densityProcess_countableFiltration_auxstatement · cited by 2
- ProbabilityTheory.Kernel.stronglyMeasurable_countableFiltration_densityProcessstatement · cited by 2