Theorems · Theorem · measure theory
MeasureTheory.generateFrom_generateSetAlgebra_eq
∀ {α : Type u_1} {𝒜 : Set (Set α)},
MeasurableSpace.generateFrom (MeasureTheory.generateSetAlgebra 𝒜) = MeasurableSpace.generateFrom 𝒜The measurable space generated by a family of sets 𝒜 is the same as the one generated
by the algebra of sets generated by 𝒜.
- Defined in
- Mathlib.MeasureTheory.SetAlgebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- MeasurableSpacestatement · cited by 13,106
- MeasurableSetproof · cited by 3,075
- le_antisymmproof · cited by 2,068
- MeasurableSet.complproof · cited by 172
- MeasurableSpace.generateFromstatement and proof · cited by 172
- MeasurableSet.iUnionproof · cited by 81
- MeasurableSet.emptyproof · cited by 58
- MeasurableSet.unionproof · cited by 55
- MeasurableSpace.measurableSet_generateFromproof · cited by 46
- MeasurableSpace.generateFrom_monoproof · cited by 15
- MeasureTheory.generateSetAlgebrastatement and proof · cited by 11
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