Theorems · Definition · functional analysis

LinearIsometryEquiv.withLpProdAssoc

(p : ENNReal) →
  (𝕜 : Type u_1) →
    (α : Type u_2) →
      (β : Type u_3) →
        (γ : Type u_4) →
          [hp : Fact (1 ≤ p)] →
            [inst : Semiring 𝕜] →
              [inst_1 : SeminormedAddCommGroup α] →
                [inst_2 : Module 𝕜 α] →
                  [inst_3 : SeminormedAddCommGroup β] →
                    [inst_4 : Module 𝕜 β] →
                      [inst_5 : SeminormedAddCommGroup γ] →
                        [inst_6 : Module 𝕜 γ] → WithLp p (WithLp p (α × β) × γ) ≃ₗᵢ[𝕜] WithLp p (α × WithLp p (β × γ))

Associativity of the L^p product as a linear isometric equivalence.

Defined in

Mathlib.Analysis.Normed.Lp.ProdLp

Cited by

2 results in Mathlib

Foundations

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

Assumes

FactSemiringSeminormedAddCommGroupModuleSeminormedAddCommGroupModuleSeminormedAddCommGroupModule