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We investigate the Baire category of $\\I$-convergent subsequences and rearrangements of $(f_n)$. Our result generalizes a theorem of Kallman. A similar theorem for subsequences is obtained if $(X,\\mu)$ is a $\\sigma$-finite complete measure space and a sequence $(f_n)$ of measurable functions from $X$ to $Z$ is $\\I$-divergent $\\mu$-almost everywhere. 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