Measure, Integration & Real Analysis · Problem 2D.17

Integration — Sheldon Axler

Mathematics — Measure Theory · cantor-set-midpoints

Problem

Let CC denote the Cantor set. Prove that {12x+12y:x,y∈C}=[0,1]\left\{\frac{1}{2}x + \frac{1}{2}y : x, y \in C\right\} = [0,1].

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