Theorems · Theorem · measure theory

MeasureTheory.Measure.restrict_biUnion_finset

∀ {α : Type u_2} {ι : Type u_6} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : ι → Set α} {T : Finset ι},
  (↑T).Pairwise (Function.onFun Disjoint s) →
    (∀ (i : ι), MeasurableSet (s i)) → μ.restrict (⋃ i ∈ T, s i) = MeasureTheory.Measure.sum fun i => μ.restrict (s ↑i)

Defined in

Mathlib.MeasureTheory.Measure.Restrict

Cited by

2 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound