`BookProof.ChapterLinftyMultiplication.memLp_top_mul` {φ ψ : α → ℂ} (hφ : MemLp φ ⊤ μ) (hψ : MemLp ψ ⊤ μ) : MemLp (fun x => φ x * ψ x) ⊤ μ

Proved

BookProof.ChapterLinftyMultiplication.memLp_top_mul

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLinftyMultiplication.

BookProof.ChapterLinftyMultiplication.memLp_top_mul {φ ψ : α → ℂ} (hφ : MemLp φ ⊤ μ) (hψ : MemLp ψ ⊤ μ) : MemLp (fun x => φ x * ψ x) ⊤ μ

Formalization note: Lean 4 identifier BookProof.ChapterLinftyMultiplication.memLp_top_mul.

Preamble

-- Generated from ChapterLinftyMultiplication.lean — theorem BookProof.ChapterLinftyMultiplication.memLp_top_mul
import Mathlib
import Definitions.Def_ChapterLinftyMultiplication
open BookProof.ChapterLinftyMultiplication


noncomputable section

open MeasureTheory ENNReal Complex


variable {α : Type*} [MeasurableSpace α] {μ : Measure α}

Formal statement

theorem BookProof.ChapterLinftyMultiplication.memLp_top_mul {φ ψ : α → ℂ} (hφ : MemLp φ ⊤ μ) (hψ : MemLp ψ ⊤ μ) :
    MemLp (fun x => φ x * ψ x) ⊤ μ := by sorry

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