lpMeasSubgroupToLpMeasIso — Mathlib

English

There is an isometric equivalence between lpSubgroup F m p μ and lpMeas F 𝕜 m p μ, preserving linear structure and norm.

Русский

Существует изометрическое эквиваленто между lpSubgroup и lpMeas, сохраняющее линейность и норму.

LaTeX

$$$lpMeasSubgroupToLpMeasIso\ F\ 𝕜\ m\ p\ μ : lpMeasSubgroup F m p μ \cong_i lpMeas F 𝕜 m p μ$$$

Lean4

/-- `lpMeasSubgroup` and `lpMeas` are isometric. -/
noncomputable def lpMeasSubgroupToLpMeasIso [Fact (1 ≤ p)] : lpMeasSubgroup F m p μ ≃ᵢ lpMeas F 𝕜 m p μ :=
  IsometryEquiv.refl (lpMeasSubgroup F m p μ)

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