Theorems · Theorem · measure theory

MeasureTheory.Measure.restrict_iUnion_ae

∀ {α : Type u_2} {ι : Type u_6} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [Countable ι] {s : ι → Set α},
  Pairwise (Function.onFun (MeasureTheory.AEDisjoint μ) s) →
    (∀ (i : ι), MeasureTheory.NullMeasurableSet (s i) μ) →
      μ.restrict (⋃ i, s i) = MeasureTheory.Measure.sum fun i => μ.restrict (s i)

Defined in

Mathlib.MeasureTheory.Measure.Restrict

Cited by

5 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Countable