  For $\sigma\in (0,+\infty)$, denote by $B_\sigma^{\infty}$ the Bernstein
space (of type $\sigma$) of all entire functions of exponential type $\leq
\sigma$ bounded on real axis $\R$. Let $I_d\subset \R$ be a segment of length
$d>0$. We announce complete description of non-uniqueness sequences of points
for $B_\sigma^\infty$ and criteria of completeness of exponential system in
$C(I_d)$ or $L^p(I_d)$ to within one or two exponential functions.
