  Small values of $|\zeta(1/2+it)|$ are investigated, using the value
distribution results of A. Selberg. This gives an asymptotic formula for
$\mu(\{0 < t \le T : |\zeta(1/2+it)| \le c\})$. Some related problems involving
values of $|\zeta(1/2+it)|$ and gaps between the consecutive ordinates of zeros
of $\zeta(s)$ are also discussed.
