Theorems · Theorem · measure theory
measurable_of_Iic
∀ {α : Type u_1} {δ : Type u_4} [inst : TopologicalSpace α] {mα : MeasurableSpace α} [BorelSpace α]
{mδ : MeasurableSpace δ} [inst_2 : LinearOrder α] [OrderTopology α] [SecondCountableTopology α] {f : δ → α},
(∀ (x : α), MeasurableSet (f ⁻¹' Set.Iic x)) → Measurable f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- LinearOrderstatement and proof · cited by 8,572
- Set.preimagestatement and proof · cited by 4,946
- MeasurableSetstatement and proof · cited by 3,075
- BorelSpacestatement and proof · cited by 1,602
- Measurablestatement · cited by 1,499
- OrderTopologystatement and proof · cited by 1,355
- Set.Iicstatement and proof · cited by 1,111
- SecondCountableTopologystatement and proof · cited by 750
- measurable_of_Ioiproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.IsStoppingTime.measurableproof · cited by 3
- MeasureTheory.isStronglyProgressive_min_stopping_timeproof · cited by 2