`BookProof.ChapterLinftyMultiplication.multOp_eq_zero_iff` [IsFiniteMeasure μ] (φ : α → ℂ) (hφ : MemLp φ ⊤ μ) : multOp φ hφ = 0 ↔ φ =ᵐ[μ] 0

Proved

BookProof.ChapterLinftyMultiplication.multOp_eq_zero_iff

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLinftyMultiplication.

BookProof.ChapterLinftyMultiplication.multOp_eq_zero_iff [IsFiniteMeasure μ] (φ : α → ℂ) (hφ : MemLp φ ⊤ μ) : multOp φ hφ = 0 ↔ φ =ᵐ[μ] 0

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

Preamble

-- Generated from ChapterLinftyMultiplication.lean — theorem BookProof.ChapterLinftyMultiplication.multOp_eq_zero_iff
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.multOp_eq_zero_iff [IsFiniteMeasure μ] (φ : α → ℂ) (hφ : MemLp φ ⊤ μ) :
    multOp φ hφ = 0 ↔ φ =ᵐ[μ] 0 := by sorry

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