Theorems · Theorem · measure theory

MeasureTheory.setLIntegral_iUnion_of_directed

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {ι : Type u_4} [Countable ι] (f : α → ENNReal)
  {s : ι → Set α}, Directed (fun x1 x2 => x1 ⊆ x2) s → ∫⁻ (x : α) in ⋃ i, s i, f x ∂μ = ⨆ i, ∫⁻ (x : α) in s i, f x ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Lebesgue.Basic

Cited by

1 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Countable