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Theorems · Theorem · measure theory

MeasurableSpace.iUnion_mem_generateMeasurableRec

∀ {α : Type u} {s : Set (Set α)} {i : Ordinal.{u_1}} {f : ℕ → Set α},
  (∀ (n : ℕ), ∃ j < i, f n ∈ MeasurableSpace.generateMeasurableRec s j) →
    ⋃ n, f n ∈ MeasurableSpace.generateMeasurableRec s i
Defined in
Mathlib.MeasureTheory.MeasurableSpace.Card
Cited by
3 results in Mathlib
Foundations
Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
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MeasurableSpace.generateMeasurableRec_mono · cited by 3MeasurableSpace.generateM…MeasurableSpace.generateMeasurable_eq_rec · cited by 2MeasurableSpace.generateM…MeasurableSpace.generateMeasurableRec_omega_one · cited by 1MeasurableSpace.generateM…Set · cited by 53352SetSet.image · cited by 5609Set.imageCompl.compl · cited by 2925Compl.complSet.iUnion · cited by 2483Set.iUnionOrdinal · cited by 1688OrdinalSet.mem_iUnion₂ · cited by 70Set.mem_iUnion₂Set.mem_union_right · cited by 18Set.mem_union_rightMeasurableSpace.generateMeasurableRec · cited by 12MeasurableSpace.generateM…MeasurableSpace.generateMeasurableRec.eq_def · cited by 5generateMeasurableRec.eq_…MeasurableSpace.iUnion_mem_ge…CITED BYCITES

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