Theorems · Theorem · functional analysis

MeasureTheory.MemLp.prod

∀ {ι : Type u_1} {α : Type u_2} {𝕜 : Type u_3} {x : MeasurableSpace α} [inst : NormedCommRing 𝕜]
  {μ : MeasureTheory.Measure α} {f : ι → α → 𝕜} {p : ι → ENNReal} {s : Finset ι},
  (∀ i ∈ s, MeasureTheory.MemLp (f i) (p i) μ) → MeasureTheory.MemLp (∏ i ∈ s, f i) (∑ i ∈ s, (p i)⁻¹)⁻¹ μ

See MemLp.prod' for the applied version.

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp

Cited by

1 results in Mathlib

Foundations

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

Assumes

NormedCommRing