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Erdős problem 120

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Let A⊆RA \subseteq \mathbb{R} be an infinite set. Must there be a set E⊆RE \subseteq \mathbb{R} of positive measure which does not contain any set of the shape a∗A+ba * A + b for some a,b∈Ra,b \in \mathbb{R} and a≠0a \neq 0?

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