Theorems · Inductive type · probability
MeasureTheory.SigmaFiniteFiltration
{Ω : Type u_1} →
{ι : Type u_2} →
{m : MeasurableSpace Ω} → [inst : Preorder ι] → MeasureTheory.Measure Ω → MeasureTheory.Filtration ι m → PropA measure is σ-finite with respect to filtration if it is σ-finite with respect to all the sub-σ-algebra of the filtration.
- Defined in
- Mathlib.Probability.Process.Filtration
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- Preorderstatement · cited by 7,952
- MeasureTheory.Filtrationstatement · cited by 425
Cited by37
Results whose statement or proof uses this declaration.
- MeasureTheory.Submartingale.expected_stoppedValue_monostatement and proof · cited by 3
- MeasureTheory.Submartingale.setIntegral_lestatement and proof · cited by 3
- MeasureTheory.martingale_martingalePartstatement and proof · cited by 2
- MeasureTheory.submartingale_of_setIntegral_lestatement and proof · cited by 2
- MeasureTheory.Martingale.eq_zero_of_predictablestatement and proof · cited by 2
- MeasureTheory.Martingale.stoppedValue_ae_eq_condExp_of_le_const_of_countable_rangestatement and proof · cited by 2
- MeasureTheory.martingale_condExpstatement and proof · cited by 1
- MeasureTheory.IsStronglyPredictable.predictablePart_eqstatement and proof · cited by 1
- MeasureTheory.martingale_const_funstatement and proof · cited by 1
- MeasureTheory.condExp_stopping_time_ae_eq_restrict_eq_of_countable_rangestatement and proof · cited by 1
- MeasureTheory.Submartingale.stoppedProcessstatement and proof · cited by 1
- MeasureTheory.Submartingale.zero_le_of_predictablestatement and proof · cited by 1