K-trivials are NCR

TL;DR

This paper proves that K-trivial reals cannot be represented as 1-random relative to any continuous probability measure, revealing a fundamental limitation in their randomness properties.

Contribution

It establishes a new connection between K-triviality and non-representability as 1-random relative to continuous measures.

Findings

K-trivial reals are not 1-random relative to any continuous measure

The result links K-triviality with measure-theoretic randomness limitations

No continuous measure can represent K-trivial reals as 1-random

Abstract

We show that for every K-trivial real X, there is no representation of a continuous probability measure m such that X is 1-random relative to m.