The Erdős similarity problem

Show that for every infinite set A of reals some set of positive measure contains no scaled and shifted copy of A.

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File it in the catalog (shoal-catalog 0521c19bbd38)

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	1	+{
	2	+ "domain": "mathematics",
	3	+ "topics": [
	4	+ "analysis"
	5	+ ],
	6	+ "type": "proof",
	7	+ "source": {
	8	+ "key": "erdos",
	9	+ "name": "Erdős Problems",
	10	+ "url": "https://www.erdosproblems.com/120",
	11	+ "id": "120",
	12	+ "curator": "Thomas Bloom",
	13	+ "poser": "Paul Erdős",
	14	+ "status": "open, $100 prize",
	15	+ "as_of": "2026-10-20",
	16	+ "prize": "$100",
	17	+ "catalog": "0521c19bbd38"
	18	+ }
	19	+}