Theorems · Theorem · measure theory

MeasureTheory.lintegral_add_left

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal},
  Measurable f → ∀ (g : α → ENNReal), ∫⁻ (a : α), f a + g a ∂μ = ∫⁻ (a : α), f a ∂μ + ∫⁻ (a : α), g a ∂μ

If f g : α → ℝ≥0∞ are two functions and one of them is (a.e.) measurable, then the Lebesgue integral of f + g equals the sum of integrals. This lemma assumes that f is integrable, see also MeasureTheory.lintegral_add_right and primed versions of these lemmas.

Defined in

Mathlib.MeasureTheory.Integral.Lebesgue.Add

Cited by

21 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound