Theorems · Theorem · probability
MeasureTheory.Filtration.rightCont_eq_of_nhdsGT_eq_bot
∀ {Ω : Type u_1} {ι : Type u_2} {m : MeasurableSpace Ω} [inst : PartialOrder ι] [inst_1 : TopologicalSpace ι]
[OrderTopology ι] (𝓕 : MeasureTheory.Filtration ι m) {i : ι}, nhdsWithin i (Set.Ioi i) = ⊥ → ↑𝓕.rightCont i = ↑𝓕 i- Defined in
- Mathlib.Probability.Process.Filtration
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- Filterstatement and proof · cited by 8,121
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement and proof · cited by 4,720
- nhdsWithinstatement and proof · cited by 1,912
- iInfproof · cited by 1,690
- Set.Ioistatement and proof · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- Filter.NeBotproof · cited by 853
- MeasureTheory.Filtrationstatement and proof · cited by 425
- MeasureTheory.Filtration.seqstatement and proof · cited by 184
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.Filtration.rightCont_eq_selfproof · cited by 0
- MeasureTheory.Filtration.rightCont_eq_of_exists_gtproof · cited by 0
- MeasureTheory.Filtration.rightCont_eq_of_isMaxproof · cited by 0