Duality between Measure and Category of Almost All Subsequences of a Given Sequence

الأصل · EN

Let S be the set of subsequences (xₙₖ) of a given real sequence (xₙ) which preserve the set of statistical cluster points. It has been recently shown that S is a set of full (Lebesgue) measure. Here, on the other hand, we prove that S is meager if and only if there exists an ordinary limit point of (xₙ) which is not a statistical cluster point of (xₙ). This provides a non-analogue between measure and category.