Theorems · Theorem · measure theory
Monotone.measurable
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] {mα : MeasurableSpace α} [BorelSpace α]
[inst_2 : TopologicalSpace β] {mβ : MeasurableSpace β} [BorelSpace β] [inst_4 : LinearOrder α] [OrderTopology α]
[SecondCountableTopology α] [inst : LinearOrder β] [OrderClosedTopology β] {f : β → α}, Monotone f → Measurable f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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.preimageproof · cited by 4,946
- Set.Iccproof · cited by 1,702
- BorelSpacestatement and proof · cited by 1,602
- Measurablestatement · cited by 1,499
- Set.Ioiproof · cited by 1,463
- Monotonestatement and proof · cited by 1,397
- OrderTopologystatement and proof · cited by 1,355
- SecondCountableTopologystatement and proof · cited by 750
- OrderClosedTopologystatement and proof · cited by 445
Cited by2
Results whose statement or proof uses this declaration.
- Antitone.measurableproof · cited by 4
- aemeasurable_restrict_of_monotoneOnproof · cited by 2