Theorems · Definition · measure theory
IsCountablySpanning
{α : Type u_1} → Set (Set α) → PropWe say that a collection of sets is countably spanning if a countable subset spans the
whole type. This is a useful condition in various parts of measure theory. For example, it is
a needed condition to show that the product of two collections generate the product sigma algebra,
see generateFrom_prod_eq.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.univproof · cited by 3,945
- Set.iUnionproof · cited by 2,483
Cited by12
Results whose statement or proof uses this declaration.
- generateFrom_eq_prodstatement and proof · cited by 5
- MeasureTheory.isCountablySpanning_spanningSetsstatement · cited by 4
- isCountablySpanning_measurableSetstatement · cited by 3
- IsCountablySpanning.null_of_forall_restrict_nullstatement and proof · cited by 3
- generateFrom_eq_pistatement and proof · cited by 3
- MeasureTheory.Measure.FiniteSpanningSetsIn.isCountablySpanningstatement · cited by 3
- MeasureTheory.Measure.forall_measure_inter_isCountablySpanning_eq_zerostatement and proof · cited by 2
- generateFrom_pi_eqstatement and proof · cited by 1
- generateFrom_prod_eqstatement and proof · cited by 1
- IsCountablySpanning.null_of_forall_inter_nullstatement and proof · cited by 1
- IsCountablySpanning.prodstatement and proof · cited by 1
- IsCountablySpanning.pistatement and proof · cited by 0