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Product of two non-measurable sets

For simplicity, assume $p = q = 1$ and $A, B \subseteq [0, 1]$. Let $\mu_k, \mu_k^{\star}$ denote the $k$-dimensional Lebesgue measure, outer measure respectively. Let $\{U(n) : n \geq 1\}$ be a seque …
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