`BookProof.NsScalarVectorCurry.lintegral_eLpNorm_slice_sq` (F : V × W → ℂ) (hF : AEStronglyMeasurable F (μ.prod ν)) : ∫⁻ x, (eLpNorm (fun y => F (x, y)) 2 ν) ^ 2 ∂μ = (eLpNorm F 2

Proved

BookProof.NsScalarVectorCurry.lintegral_eLpNorm_slice_sq

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsScalarVectorCurry.

BookProof.NsScalarVectorCurry.lintegral_eLpNorm_slice_sq (F : V × W → ℂ) (hF : AEStronglyMeasurable F (μ.prod ν)) : ∫⁻ x, (eLpNorm (fun y => F (x, y)) 2 ν) ^ 2 ∂μ = (eLpNorm F 2 (μ.prod ν)) ^ 2

Formalization note: Lean 4 identifier BookProof.NsScalarVectorCurry.lintegral_eLpNorm_slice_sq.

Preamble

-- Generated from ChapterNsScalarVectorCurry.lean — theorem BookProof.NsScalarVectorCurry.lintegral_eLpNorm_slice_sq
import Mathlib
import Definitions.Def_ChapterNsScalarVectorCurry
open BookProof.NsScalarVectorCurry


open MeasureTheory Filter Set
open scoped ENNReal ComplexConjugate


noncomputable section

variable {V W : Type*} [MeasurableSpace V] [MeasurableSpace W]
  {μ : Measure V} {ν : Measure W}

variable [SigmaFinite μ] [SigmaFinite ν]

Formal statement

theorem BookProof.NsScalarVectorCurry.lintegral_eLpNorm_slice_sq (F : V × W → ℂ) (hF : AEStronglyMeasurable F (μ.prod ν)) :
    ∫⁻ x, (eLpNorm (fun y => F (x, y)) 2 ν) ^ 2 ∂μ = (eLpNorm F 2 (μ.prod ν)) ^ 2 := by sorry

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