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Let $S$ be the set of subsequences $(x_{n_k})$ of a given real sequence$(x_n)$ which preserve the set of statistical cluster points. It has beenrecently shown that $S$ is a set of full (Lebesgue) measure. Here, on the otherhand, we prove that $S$ is meager if and only if there exists an ordinary limitpoint of $(x_n)$ which is not a statistical cluster point of $(x_n)$. Thisprovides a non-analogue between measure and category.

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