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Theorems · Theorem · measure theory

MeasurableSpace.DynkinSystem.has_compl

∀ {α : Type u_4} (self : MeasurableSpace.DynkinSystem α) {a : Set α}, self.Has a → self.Has aᶜ

A Dynkin system is closed under complementation.

Defined in
Mathlib.MeasureTheory.PiSystem
Cited by
4 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
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Around this declaration

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

MeasurableSpace.DynkinSystem.generate_le · cited by 3DynkinSystem.generate_leMeasurableSpace.DynkinSystem.toMeasurableSpace · cited by 2DynkinSystem.toMeasurable…MeasurableSpace.DynkinSystem.has_compl_iff · cited by 1DynkinSystem.has_compl_iffMeasurableSpace.DynkinSystem.has_sdiff · cited by 1DynkinSystem.has_sdiffMeasurableSpace.DynkinSystem.has_univ · cited by 0DynkinSystem.has_univSet · cited by 53352SetCompl.compl · cited by 2925Compl.complMeasurableSpace.DynkinSystem · cited by 19MeasurableSpace.DynkinSys…MeasurableSpace.DynkinSystem.Has · cited by 17DynkinSystem.HasDynkinSystem.has_complCITED BYCITES

Cites4

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Cited by5

Results whose statement or proof uses this declaration.