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Theorems · Theorem · measure theory

MeasureTheory.restrict_Ioi_eq_restrict_Ici

∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasureTheory.NullSingletonClass μ]
  [inst : PartialOrder α] {a : α}, μ.restrict (Set.Ioi a) = μ.restrict (Set.Ici a)
Defined in
Mathlib.MeasureTheory.Measure.Typeclasses.NullSingletonClass
Cited by
1 results in Mathlib
Foundations
Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasureTheory.NullSingletonClassPartialOrder
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Around this declaration

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

not_integrableOn_Ioi_inv · cited by 2not_integrableOn_Ioi_invMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasurePartialOrder · cited by 6410PartialOrderMeasureTheory.Measure.restrict · cited by 1646Measure.restrictSet.Ioi · cited by 1463Set.IoiSet.Ici · cited by 1070Set.IciMeasureTheory.NullSingletonClass · cited by 125MeasureTheory.NullSinglet…MeasureTheory.Measure.restrict_congr_set · cited by 43Measure.restrict_congr_setMeasureTheory.Ioi_ae_eq_Ici · cited by 5MeasureTheory.Ioi_ae_eq_I…MeasureTheory.restrict_Ioi_eq…CITED BYCITES

Cites9

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Cited by1

Results whose statement or proof uses this declaration.