Absztrakt: | The double series (1) $\sum\sp \infty\sb{m=1}\sum\sp \infty\sb{n=1}
a\sb{mn}\varphi\sb{mn}(x)$ is considered, where $\{a\sb{mn}\}$
is a double sequence of real numbers $\Phi=\{\varphi\sb{mn}(x);
m,n=1,2,\dots\}$ is a double system of measurable functions defined
on a finite positive measure space $(X,{\cal F},\mu)$.\par
It
is assumed that the series (1) convergences or is Ces\`aro summable
on a set of positive measure or almost everywhere (in Pringsheim's
or regular sense).\par
Hence properties of $\{a\sb{mn}\}$ $(m,n=1,2,\dots)$
are concluded.}
\RV{B.Osilenker (Moskva) |