Theorems · Definition · measure theory

MeasureTheory.Measure.ofMeasurable

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

Obtain a measure by giving a countably additive function that sends ∅ to 0.

Defined in

Mathlib.MeasureTheory.Measure.MeasureSpaceDef

Cited by

4 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace