Theorems · Theorem · measure theory

MeasureTheory.ae_restrict_uIoc_eq

∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : LinearOrder α] (a b : α),
  MeasureTheory.ae (μ.restrict (Set.uIoc a b)) =
    MeasureTheory.ae (μ.restrict (Set.Ioc a b)) ⊔ MeasureTheory.ae (μ.restrict (Set.Ioc b a))

Defined in: Mathlib.MeasureTheory.Measure.Restrict
Cited by: 1 results in Mathlib
Foundations: Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder

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Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
LinearOrderstatement and proof · cited by 8,572
Filterstatement · cited by 8,121
MeasureTheory.aestatement and proof · cited by 2,352
MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
Set.Iocstatement and proof · cited by 971
Set.uIocstatement and proof · cited by 182
MeasureTheory.ae.congr_simpproof · cited by 39
Set.uIoc_eq_unionproof · cited by 8
MeasureTheory.ae_restrict_union_eqproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.ae_restrict_uIoc_iffproof · cited by 2