An uncountable subset of the real numbers whose intersection with every null set for Lebesgue measure is countable. Testing only Borel sets suffices because every Lebesgue-null set has a Borel null superset. No measurability of is assumed.
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The Sierpiński set typically refers to a specific type of fractal set known as the Sierpiński triangle (or Sierpiński gasket) or the Sierpiński carpet. Both are examples of Sierpiński sets, which are created by recursively removing triangles or squares, respectively, from a larger shape. ### Sierpiński Triangle 1. **Construction**: Start with an equilateral triangle.