Theorems · Theorem · measure theory
measurable_of_Ioi
∀ {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.Ioi x)) → Measurable f- Cited by
- 4 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- 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
- Set.rangeproof · cited by 4,705
- MeasurableSetstatement and proof · cited by 3,075
- BorelSpacestatement and proof · cited by 1,602
- Measurablestatement and proof · cited by 1,499
- Set.Ioistatement and proof · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- SecondCountableTopologystatement and proof · cited by 750
Cited by4
Results whose statement or proof uses this declaration.
- LowerSemicontinuous.measurableproof · cited by 4
- Monotone.measurableproof · cited by 2
- measurable_of_Iicproof · cited by 2
- measurable_iSup_of_lowerSemicontinuousproof · cited by 1