`BookProof.ChapterLinftyMultiplication.unitInterval_atomless` (x : ℝ) : (MeasureTheory.volume.restrict (Set.Icc (0 : ℝ) 1)) {x} = 0

Proved

BookProof.ChapterLinftyMultiplication.unitInterval_atomless

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLinftyMultiplication.

BookProof.ChapterLinftyMultiplication.unitInterval_atomless (x : ℝ) : (MeasureTheory.volume.restrict (Set.Icc (0 : ℝ) 1)) {x} = 0

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

Preamble

-- Generated from ChapterLinftyMultiplication.lean — theorem BookProof.ChapterLinftyMultiplication.unitInterval_atomless
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.unitInterval_atomless (x : ℝ) :
    (MeasureTheory.volume.restrict (Set.Icc (0 : ℝ) 1)) {x} = 0 := by sorry

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