Theorems · Theorem · measure theory

MeasureTheory.eLpNorm_sum_le

∀ {α : Type u_1} {ε' : Type u_4} {m : MeasurableSpace α} [inst : TopologicalSpace ε']
  [inst_1 : ESeminormedAddCommMonoid ε'] {p : ENNReal} {μ : MeasureTheory.Measure α} [ContinuousAdd ε'] {ι : Type u_5}
  {f : ι → α → ε'} {s : Finset ι},
  (∀ i ∈ s, MeasureTheory.AEStronglyMeasurable (f i) μ) →
    1 ≤ p → MeasureTheory.eLpNorm (∑ i ∈ s, f i) p μ ≤ ∑ i ∈ s, MeasureTheory.eLpNorm (f i) p μ

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality

Cited by

2 results in Mathlib

Foundations

Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceESeminormedAddCommMonoidContinuousAdd