  A bounded Kolmogorov-Loveland selection rule is an adaptive strategy for
recursively selecting a subsequence of an infinite binary sequence; such a
subsequence may be interpreted as the query sequence of a time-bounded Turing
machine. In this paper we show that if A is an algorithmically random sequence,
A_0 is selected from A via a bounded Kolmogorov-Loveland selection rule, and
A_1 denotes the sequence of nonselected bits of A, then A_1 is independent of
A_0; that is, A_1 is algorithmically random relative to A_0. This result has
been used by Kautz and Miltersen [1] to show that relative to a random oracle,
NP does not have p-measure zero (in the sense of Lutz [2]).
  [1] S. M. Kautz and P. B. Miltersen. Relative to a random oracle, NP is not
small. Journal of Computer and System Sciences, 53:235-250, 1996.
  [2] J. H. Lutz. Almost everywhere high nonuniform complexity. Journal of
Computer and System Sciences, 44:220-258, 1992.
