Theorems · Theorem · measure theory

MeasureTheory.lintegral_union

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal} {A B : Set α},
  MeasurableSet B → Disjoint A B → ∫⁻ (a : α) in A ∪ B, f a ∂μ = ∫⁻ (a : α) in A, f a ∂μ + ∫⁻ (a : α) in B, f a ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Lebesgue.Basic

Cited by

5 results in Mathlib

Foundations

Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound