  Let $\I$ be an ideal on $\N$ which is either analytic or coanalytic. Assume
that $(f_n)$ is a sequence of functions with the Baire property from a Polish
space $X$ into a complete metric space $Z$, which is divergent on a comeager
set. 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. Then the set of subsequences
of $(f_n)$, $\I$-divergent $\mu$-almost everywhere, is of full product measure
on $\{ 0,1\}^\N$. Here we assume additionally that $\mathcal I$ has property
(G).
