  The problem of minimax detection of Gaussian random signal vector in White
Gaussian additive noise is considered. It is supposed that an unknown vector
$\boldsymbol{\sigma}$ of the signal vector intensities belong to the given set
${\mathcal E}$. It is investigated when it is possible to replace the set
${\mathcal E}$ by a smaller set ${\mathcal E}_{0}$ without loss of quality
(and, in particular, to replace it by a single point
$\boldsymbol{\sigma}_{0}$).
