Theorems · Theorem · measure theory

MeasureTheory.Measure.univ_pi_Ioo_ae_eq_Icc

∀ {ι : Type u_1} {α : ι → Type u_3} [inst : Fintype ι] [inst_1 : (i : ι) → MeasurableSpace (α i)]
  {μ : (i : ι) → MeasureTheory.Measure (α i)} [∀ (i : ι), MeasureTheory.SigmaFinite (μ i)]
  [inst_3 : (i : ι) → PartialOrder (α i)] [∀ (i : ι), MeasureTheory.NullSingletonClass (μ i)] {f g : (i : ι) → α i},
  (Set.univ.pi fun i => Set.Ioo (f i) (g i)) =ᵐ[MeasureTheory.Measure.pi μ] Set.Icc f g

Defined in

Mathlib.MeasureTheory.Constructions.Pi

Cited by

2 results in Mathlib

Foundations

Depth 236 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeMeasurableSpaceMeasureTheory.SigmaFinitePartialOrderMeasureTheory.NullSingletonClass