Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.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} [T2Space M],
  (∀ (i : β), MeasurableSet (f i)) → Pairwise (Function.onFun Disjoint f) → v (⋃ i, f i) = ∑' (i : β), v (f i)

Defined in

Mathlib.MeasureTheory.VectorMeasure.Basic

Cited by

9 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpaceCountableT2Space