Theorems · Theorem · measure theory
MeasurableSpace.cardinal_generateMeasurable_le_continuum
∀ {α : Type u} {s : Set (Set α)},
Cardinal.mk ↑s ≤ Cardinal.continuum → Cardinal.mk ↑{t | MeasurableSpace.GenerateMeasurable s t} ≤ Cardinal.continuumIf a sigma-algebra is generated by a set of sets s with cardinality at most the continuum,
then the sigma algebra has the same cardinality bound.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 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
- Set.Elemstatement and proof · cited by 7,166
- Set.ofPredstatement · cited by 6,101
- LE.le.transproof · cited by 3,151
- Cardinalstatement and proof · cited by 2,598
- LT.lt.leproof · cited by 2,189
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.aleph0proof · cited by 521
- max_leproof · cited by 71
- Cardinal.continuumstatement and proof · cited by 60
- MeasurableSpace.GenerateMeasurablestatement · cited by 11
- Cardinal.power_le_power_rightproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- MeasurableSpace.cardinal_measurableSet_le_continuumproof · cited by 0