  The Bernoulli sieve is a random allocation scheme obtained by placing
independent points with the uniform [0,1] law into the intervals made up by
successive positions of a multiplicative random walk with factors taking values
in the interval (0,1). Assuming that the number of points is equal to n we
investigate the weak convergence, as n tends to infinity, of finite-dimensional
distributions of the number of empty intervals within the occupancy range. A
new argument enables us to relax the constraints imposed in previous papers on
the distribution of the factor of the multiplicative random walk.

Probability