Theorems · Theorem · measure theory

MeasureTheory.measure_biUnion_null_iff

∀ {α : Type u_1} {ι : Type u_2} {F : Type u_3} [inst : FunLike F (Set α) ENNReal] [MeasureTheory.OuterMeasureClass F α]
  {μ : F} {I : Set ι}, I.Countable → ∀ {s : ι → Set α}, μ (⋃ i ∈ I, s i) = 0 ↔ ∀ i ∈ I, μ (s i) = 0

Defined in

Mathlib.MeasureTheory.OuterMeasure.Basic

Cited by

11 results in Mathlib

Foundations

Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FunLikeMeasureTheory.OuterMeasureClass