All Sampling Methods Produce Outliers.

Given a computable probability measure $P$ over natural numbers or infinite binary sequences, there is no computable, randomized method that can produce an arbitrarily large sample such that none of its members are outliers of $P$. In addition, given a binary predicate $\gamma $ , the length of the smallest program that computes a complete extension of $\gamma $ is less than the size of the domain of $\gamma $ plus the amount of information that $\gamma $ has with the halting sequence. [ABSTRACT FROM AUTHOR]