Abstract: Let be a sequence of independent identically distributed random
vectors with values in a Banach space weak mean zero and weak second moment. Let
and let be the unit ball of the reproducing kernel Hilbert space
associated with We show that for any infinie set of positive integers the
cluster set of equals almost surely where
satisfies and can be determined in terms of and by the convergence of
certain series.
be a sequence of independent identically distributed random
vectors with values in a Banach space 
weak mean zero and weak second moment. Let
and let 
be the unit ball of the reproducing kernel Hilbert space
associated with 
We show that for any infinie set 
of positive integers the
cluster set of 
equals almost surely 
where 
satisfies 
and can be determined in terms of 
and 
by the convergence of
certain series.