TL;DR
The paper proves that no computable randomized sampling method can generate arbitrarily large samples free of outliers for a given computable probability measure over natural numbers or infinite binary sequences.
Contribution
It establishes a fundamental limitation on computable sampling methods in avoiding outliers in large samples.
Findings
No computable randomized method can produce arbitrarily large outlier-free samples.
The result applies to measures over natural numbers and infinite binary sequences.
It highlights inherent constraints in algorithmic sampling processes.
Abstract
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.
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