Theorems · Theorem · measure theory

MeasureTheory.Measure.ae_eq_set_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)] {I : Set ι}
  {s t : (i : ι) → Set (α i)}, (∀ i ∈ I, s i =ᵐ[μ i] t i) → I.pi s =ᵐ[MeasureTheory.Measure.pi μ] I.pi t

Defined in

Mathlib.MeasureTheory.Constructions.Pi

Cited by

9 results in Mathlib

Foundations

Depth 234 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeMeasurableSpaceMeasureTheory.SigmaFinite