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Theorems · Theorem · measure theory

isPiSystem_iUnion_of_monotone

∀ {α : Type u_3} {ι : Type u_4} [inst : SemilatticeSup ι] (p : ι → Set (Set α)),
  (∀ (n : ι), IsPiSystem (p n)) → Monotone p → IsPiSystem (⋃ n, p n)
Defined in
Mathlib.MeasureTheory.PiSystem
Cited by
2 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemilatticeSup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ProbabilityTheory.Kernel.setIntegral_density · cited by 2Kernel.setIntegral_densityMeasureTheory.Integrable.tendsto_ae_condExp · cited by 2Integrable.tendsto_ae_con…Set · cited by 53352SetSet.iUnion · cited by 2483Set.iUnionMonotone · cited by 1397MonotoneSemilatticeSup · cited by 785SemilatticeSupIsPiSystem · cited by 88IsPiSystemMonotone.directed_le · cited by 25Monotone.directed_leisPiSystem_iUnion_of_directed_le · cited by 2isPiSystem_iUnion_of_dire…isPiSystem_iUnion_of_monotoneCITED BYCITES

Cites7

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Cited by2

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