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It is known that for any $f\\in B\\_{p,q}^s(\\mathbb{R}^N)$ with $q\\leq p$ we have $f(\\cdot,y)\\in B\\_{p,q}^s(\\mathbb{R}^d)$ for a.e. $y\\in \\mathbb{R}^{N-d}$. We prove that this is no longer true when $p\\<q$. Namely, we construct a function $f\\in B\\_{p,q}^s(\\mathbb{R}^N)$ such that $f(\\cdot,y)\\notin B\\_{p,q}^s(\\mathbb{R}^d)$ for a.e. $y\\in \\mathbb{R}^{N-d}$. 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