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Theorems · Theorem · measure theory

MeasurableSpace.measurableSet_empty

∀ {α : Type u_7} (self : MeasurableSpace α), MeasurableSpace.MeasurableSet' self ∅

The empty set is a measurable set. Use MeasurableSet.empty instead.

Defined in
Mathlib.MeasureTheory.MeasurableSpace.Defs
Cited by
5 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
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Around this declaration

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

MeasurableSet.empty · cited by 58MeasurableSet.emptyMeasurableSpace.map · cited by 23MeasurableSpace.mapMeasurableSpace.invariants · cited by 8MeasurableSpace.invariantsMeasurableSpace.generateFrom_induction · cited by 7MeasurableSpace.generateF…MeasurableSpace.DynkinSystem.ofMeasurableSpace · cited by 4DynkinSystem.ofMeasurable…MeasurableSpace.measurableSet_bot_iff · cited by 2MeasurableSpace.measurabl…MeasureTheory.Filtration.filtrationOfSet_eq_natural · cited by 1Filtration.filtrationOfSe…MeasureTheory.generateFrom_generateSetAlgebra_eq · cited by 0MeasureTheory.generateFro…Set · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasurableSpace.MeasurableSet' · cited by 4MeasurableSpace.Measurabl…MeasurableSpace.measurableSet…CITED BYCITES

Cites3

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Cited by8

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