Measure, Integration & Real Analysis · Problem 2A.13

Measures — Sheldon Axler

Mathematics — Measure Theory · outer-measure-closed-irrational-set

Problem

Suppose ε>0\varepsilon > 0. Prove that there exists a subset FF of [0,1][0, 1] such that FF is closed, every element of FF is an irrational number, and ∣F∣>1−ε|F| > 1 - \varepsilon.

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