  This paper presents results about the distribution of subsequences which are
typical in the sense of Baire.
  The first part is concerned with sequences of the type x_k = n_k*alpha, n_1 <
n_2 < n_3 < ..., mod 1. Improving a result of Salat we show that, if the
quotients q_k = n_{k+1}/n_k satisfy q_k > 1+ epsilon, then the set of alpha
such that (x_k) is uniformly distributed is of first Baire category, i.e. for
generic alpha we do not have uniform distribution. Under the stronger
assumption lim q_k = infinity one even has maldistribution for generic alpha,
the strongest possible contrast to uniform distribution.
  The second part reverses the point of view by considering appropriately
defined Baire spaces S of subsequences. For a fixed well distributed sequence
(x_n) we show that there is a set M of measures such that for generic (n_k) in
S the set of limit measures of the subsequence (x_{n_k}) is exactly M.

Number Theory;Dynamical Systems