Theorems · Theorem · measure theory
borel_eq_generateFrom_Icc
∀ (α : Type u_5) [inst : TopologicalSpace α] [SecondCountableTopology α] [inst_2 : LinearOrder α] [OrderTopology α],
borel α = MeasurableSpace.generateFrom {S | ∃ l u, l ≤ u ∧ Set.Icc l u = S}- Cited by
- 1 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.
Cites15
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 · cited by 13,106
- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredstatement and proof · cited by 6,101
- Set.Iccstatement and proof · cited by 1,702
- OrderTopologystatement and proof · cited by 1,355
- Set.Iooproof · cited by 1,214
- SecondCountableTopologystatement and proof · cited by 750
- Set.mem_univproof · cited by 416
- MeasurableSpace.generateFromstatement and proof · cited by 172
- IsBotproof · cited by 77
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.ext_of_Icc'proof · cited by 1