Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.hasSum_of_disjoint_iUnion

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {M : Type u_3} [inst : AddCommMonoid M]
  [inst_1 : TopologicalSpace M] [Countable β] {v : MeasureTheory.VectorMeasure α M} {f : β → Set α},
  (∀ (i : β), MeasurableSet (f i)) → Pairwise (Function.onFun Disjoint f) → HasSum (fun i => v (f i)) (v (⋃ i, f i))

Defined in

Mathlib.MeasureTheory.VectorMeasure.Basic

Cited by

2 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpaceCountable