Theorems · Theorem · measure theory
Set.OrdConnected.measurableSet
∀ {α : Type u_1} {s : Set α} [inst : TopologicalSpace α] {mα : MeasurableSpace α} [OpensMeasurableSpace α]
[inst_2 : LinearOrder α] [OrderClosedTopology α], s.OrdConnected → MeasurableSet s- Cited by
- 4 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · 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
- LE.le.transproof · cited by 3,151
- MeasurableSetstatement and proof · cited by 3,075
- Set.iUnionproof · cited by 2,483
- IsOpenproof · cited by 2,400
- Set.Finiteproof · cited by 1,814
- Set.Iooproof · cited by 1,214
- OpensMeasurableSpacestatement and proof · cited by 636
- OrderClosedTopologystatement and proof · cited by 445
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAtproof · cited by 3
- Monotone.measurableproof · cited by 2
- MeasurableSet.image_of_monotoneOn_of_continuousOnproof · cited by 1
- IsPreconnected.measurableSetproof · cited by 0