Theorems · Theorem · measure theory

MeasureTheory.inducedOuterMeasure_eq

∀ {α : Type u_1} [inst : MeasurableSpace α] {m : (s : Set α) → MeasurableSet s → ENNReal} (m0 : m ∅ ⋯ = 0),
  (∀ ⦃f : ℕ → Set α⦄ (hm : ∀ (i : ℕ), MeasurableSet (f i)),
      Pairwise (Function.onFun Disjoint f) → m (⋃ i, f i) ⋯ = ∑' (i : ℕ), m (f i) ⋯) →
    ∀ {s : Set α} (hs : MeasurableSet s), (MeasureTheory.inducedOuterMeasure m ⋯ m0) s = m s hs

Defined in

Mathlib.MeasureTheory.OuterMeasure.Induced

Cited by

1 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace