Fatou lemma for series
= Fatou lemma for series
{c}
For nonnegative numbers $a_{n,k}$, <Fatou lemma> applied to counting measure gives
$$
\sum_k\liminf_{n\to\infty}a_{n,k}
\leq\liminf_{n\to\infty}\sum_ka_{n,k}.
$$
= Fatou lemma for series
{c}
For nonnegative numbers $a_{n,k}$, <Fatou lemma> applied to counting measure gives
$$
\sum_k\liminf_{n\to\infty}a_{n,k}
\leq\liminf_{n\to\infty}\sum_ka_{n,k}.
$$