`BookProof.ChapterMeasureAtomicDiffuse.mem_atomSet_iff` (x : α) : x ∈ atomSet mu ↔ mu {x} ≠ 0

Proved

BookProof.ChapterMeasureAtomicDiffuse.mem_atomSet_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMeasureAtomicDiffuse.

BookProof.ChapterMeasureAtomicDiffuse.mem_atomSet_iff (x : α) : x ∈ atomSet mu ↔ mu {x} ≠ 0

Formalization note: Lean 4 identifier BookProof.ChapterMeasureAtomicDiffuse.mem_atomSet_iff.

Preamble

-- Generated from ChapterMeasureAtomicDiffuse.lean — theorem BookProof.ChapterMeasureAtomicDiffuse.mem_atomSet_iff
import Mathlib
import Definitions.Def_ChapterMeasureAtomicDiffuse
open BookProof.ChapterMeasureAtomicDiffuse


noncomputable section

open MeasureTheory Complex



variable {α : Type*} [MeasurableSpace α] [MeasurableSingletonClass α] (mu : Measure α)

Formal statement

theorem BookProof.ChapterMeasureAtomicDiffuse.mem_atomSet_iff (x : α) : x ∈ atomSet mu ↔ mu {x} ≠ 0 := by sorry

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