  Let v, w be infinite 0-1 sequences, and m a positive integer. We say that w
is m-embeddable in v, if there exists an increasing sequence n_{i} of integers
with n_{0}=0, such that 0< n_{i} - n_{i-1} < m, w(i) = v(n_i) for all i > 0.
Let X and Y be independent coin-tossing sequences. We will show that there is
an m with the property that Y is m-embeddable into X with positive probability.
This answers a question that was open for a while. The proof generalizes
somewhat the hierarchical method of an earlier paper of the author on dependent
percolation.
