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.