# Recent progress on conditional randomness

## TL;DR

This paper reviews recent advances in the study of ML-randomness conditioned on probabilities, highlighting a new result that generalizes previous work for mutually singular measures.

## Contribution

It introduces a novel result on conditional randomness with respect to mutually singular probabilities, extending Hanssen's 2010 findings for Bernoulli processes.

## Key findings

- New result on conditional randomness for mutually singular probabilities
- Generalization of Hanssen's 2010 result for Bernoulli processes
- Advances in understanding ML-randomness with respect to conditional measures

## Abstract

In this article, recent progress on ML-randomness with respect to conditional probabilities is reviewed. In particular a new result of conditional randomness with respect to mutually singular probabilities are shown, which is a generalization of Hanssen's result (2010) for Bernoulli processes.