Theorems · Theorem · measure theory
borel_eq_generateFrom_Ioi
∀ (α : Type u_1) [inst : TopologicalSpace α] [SecondCountableTopology α] [inst_2 : LinearOrder α] [OrderTopology α], borel α = MeasurableSpace.generateFrom (Set.range Set.Ioi)
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement · cited by 13,106
- LinearOrderstatement and proof · cited by 8,572
- Set.rangestatement · cited by 4,705
- Set.Ioistatement · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- OrderDualproof · cited by 927
- SecondCountableTopologystatement and proof · cited by 750
- MeasurableSpace.generateFromstatement · cited by 172
- borelstatement · cited by 57
- borel_eq_generateFrom_Iioproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- measurable_of_Ioiproof · cited by 4
- borel_eq_generateFrom_Iicproof · cited by 4
- Measurable.isLUBproof · cited by 3
- Real.borel_eq_generateFrom_Ioi_ratproof · cited by 1
- StieltjesFunction.borel_le_measurableproof · cited by 0