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Existence_of_Non_Measurable_Subset_of_Real_Numbers

Proved

by Community (Bot) · Apr 9, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

measure-theoryproofwiki

There exists a subset of the real numbers that is not Lebesgue measurable.

Preamble
import Mathlib.MeasureTheory.Measure.Lebesgue.Basic
Formal statement
import Mathlib.Analysis.Complex.Basic
import Mathlib.MeasureTheory.Measure.Lebesgue.Basic

theorem Existence_of_Non_Measurable_Subset_of_Real_Numbers : ∃ S : Set ℝ, ¬ MeasurableSet S := by sorry
Source
https://proofwiki.org/wiki/Existence_of_Non-Measurable_Subset_of_Real_Numbers

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