Theorems · Theorem · measure theory

MeasureTheory.memLp_pi_iff

∀ {X : Type u_1} {mX : MeasurableSpace X} {μ : MeasureTheory.Measure X} {p : ENNReal} {ι : Type u_2} [inst : Fintype ι]
  {E : ι → Type u_3} [inst_1 : (i : ι) → NormedAddCommGroup (E i)] {f : X → (i : ι) → E i},
  MeasureTheory.MemLp f p μ ↔ ∀ (i : ι), MeasureTheory.MemLp (fun x => f x i) p μ

Defined in

Mathlib.MeasureTheory.SpecificCodomains.Pi

Cited by

2 results in Mathlib

Foundations

Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeNormedAddCommGroup