Theorems · Theorem · measure theory

MeasureTheory.setLIntegral_max

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : α → ENNReal},
  Measurable f →
    Measurable g →
      ∀ (s : Set α),
        ∫⁻ (x : α) in s, max (f x) (g x) ∂μ =
          ∫⁻ (x : α) in s ∩ {x | f x ≤ g x}, g x ∂μ + ∫⁻ (x : α) in s ∩ {x | g x < f x}, f x ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Lebesgue.Basic

Cited by

1 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound