Theorems · Theorem · measure theory

MeasureTheory.isSigmaSubadditive_of_addContent_iUnion_eq_tsum

∀ {α : Type u_1} {C : Set (Set α)} {m : MeasureTheory.AddContent ENNReal C},
  MeasureTheory.IsSetRing C →
    (∀ (f : ℕ → Set α),
        (∀ (i : ℕ), f i ∈ C) →
          ⋃ i, f i ∈ C → Pairwise (Function.onFun Disjoint f) → m (⋃ i, f i) = ∑' (i : ℕ), m (f i)) →
      m.IsSigmaSubadditive

If an additive content is σ-additive on a set ring, then it is σ-subadditive.

Defined in

Mathlib.MeasureTheory.Measure.AddContent

Cited by

2 results in Mathlib

Foundations

Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound