Theorems · Theorem · measure theory

MeasureTheory.memLp_prod_iff

∀ {X : Type u_1} {mX : MeasurableSpace X} {μ : MeasureTheory.Measure X} {p : ENNReal} {E : Type u_2} {F : Type u_3}
  [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F] {f : X → E × F},
  MeasureTheory.MemLp f p μ ↔ MeasureTheory.MemLp (fun x => (f x).1) p μ ∧ MeasureTheory.MemLp (fun x => (f x).2) p μ

Defined in

Mathlib.MeasureTheory.SpecificCodomains.Pi

Cited by

3 results in Mathlib

Foundations

Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroup