Theorems · Theorem · measure theory

MeasureTheory.lpNorm_expect_le

∀ {α : Type u_1} {E : Type u_2} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] [inst_1 : Module ℚ≥0 E] [NormedSpace ℝ E] {ι : Type u_3} {s : Finset ι} {f : ι → α → E},
  (∀ i ∈ s, MeasureTheory.MemLp (f i) p μ) →
    1 ≤ p → MeasureTheory.lpNorm (s.expect fun i => f i) p μ ≤ s.expect fun i => MeasureTheory.lpNorm (f i) p μ

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.LpNorm

Cited by

0 results in Mathlib

Foundations

Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupModuleNormedSpace