Theorems · Theorem · measure theory

MeasureTheory.lintegral_edist_triangle

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  {f g h : α → β},
  MeasureTheory.AEStronglyMeasurable f μ →
    MeasureTheory.AEStronglyMeasurable h μ →
      ∫⁻ (a : α), edist (f a) (g a) ∂μ ≤ ∫⁻ (a : α), edist (f a) (h a) ∂μ + ∫⁻ (a : α), edist (g a) (h a) ∂μ

Defined in

Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral

Cited by

1 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroup