Theorems · Theorem · measure theory

MeasureTheory.ae_uIoc_iff

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : LinearOrder α] {a b : α} {P : α → Prop},
  (∀ᵐ (x : α) ∂μ, x ∈ Set.uIoc a b → P x) ↔
    (∀ᵐ (x : α) ∂μ, x ∈ Set.Ioc a b → P x) ∧ ∀ᵐ (x : α) ∂μ, x ∈ Set.Ioc b a → P x

See also MeasureTheory.ae_restrict_uIoc_iff.

Defined in

Mathlib.MeasureTheory.Measure.MeasureSpace

Cited by

1 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrder