Theorems · Theorem · measure theory

MeasureTheory.lintegral_iUnion_le

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [Countable β] (s : β → Set α)
  (f : α → ENNReal), ∫⁻ (a : α) in ⋃ i, s i, f a ∂μ ≤ ∑' (i : β), ∫⁻ (a : α) in s i, f a ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Lebesgue.Basic

Cited by

2 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Countable