`BookProof.ChapterAbelianMixture.mixtureMeasure_not_purely_atomic_on_Icc` : 0 < mixtureMeasure (Set.Icc (0 : ℝ) 1) ∧ ∀ x ∈ Set.Icc (0 : ℝ) 1, mixtureMeasure {x} = 0

Proved

BookProof.ChapterAbelianMixture.mixtureMeasure_not_purely_atomic_on_Icc

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianMixture.

BookProof.ChapterAbelianMixture.mixtureMeasure_not_purely_atomic_on_Icc : 0 < mixtureMeasure (Set.Icc (0 : ℝ) 1) ∧ ∀ x ∈ Set.Icc (0 : ℝ) 1, mixtureMeasure {x} = 0

Formalization note: Lean 4 identifier BookProof.ChapterAbelianMixture.mixtureMeasure_not_purely_atomic_on_Icc.

Preamble

-- Generated from ChapterAbelianMixture.lean — theorem BookProof.ChapterAbelianMixture.mixtureMeasure_not_purely_atomic_on_Icc
import Mathlib
import Definitions.Def_ChapterAbelianMixture
open BookProof.ChapterAbelianMixture


noncomputable section

open MeasureTheory ENNReal

Formal statement

theorem BookProof.ChapterAbelianMixture.mixtureMeasure_not_purely_atomic_on_Icc :
    0 < mixtureMeasure (Set.Icc (0 : ℝ) 1) ∧
      ∀ x ∈ Set.Icc (0 : ℝ) 1, mixtureMeasure {x} = 0 := by sorry

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