Theorems · Theorem · measure theory

MeasureTheory.exists_null_pairwise_disjoint_sdiff

∀ {ι : Type u_1} {α : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [Countable ι] {s : ι → Set α},
  Pairwise (Function.onFun (MeasureTheory.AEDisjoint μ) s) →
    ∃ t,
      (∀ (i : ι), MeasurableSet (t i)) ∧
        (∀ (i : ι), μ (t i) = 0) ∧ Pairwise (Function.onFun Disjoint fun i => s i \ t i)

If s : ι → Set α is a countable family of pairwise a.e. disjoint sets, then there exists a family of measurable null sets t i such that s i \ t i are pairwise disjoint.

Defined in

Mathlib.MeasureTheory.Measure.AEDisjoint

Cited by

2 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Countable