Theorems · Theorem · measure theory

MeasureTheory.Measure.ae_eq_pi

∀ {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)] {β : ι → Type u_4}
  {f f' : (i : ι) → α i → β i},
  (∀ (i : ι), f i =ᵐ[μ i] f' i) → (fun x i => f i (x i)) =ᵐ[MeasureTheory.Measure.pi μ] fun x i => f' i (x i)

Defined in

Mathlib.MeasureTheory.Constructions.Pi

Cited by

0 results in Mathlib

Foundations

Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeMeasurableSpaceMeasureTheory.SigmaFinite