Algorithmic randomness theory starts with a notion of an individual random object. To be
reasonable, this notion should have some natural properties; in particular, an object should …

We continue the investigation of algorithmically random functions and closed sets, and in
particular the connection with the notion of capacity. We study notions of random continuous …

A tree is pathwise-random if all of its paths are Martin-Löf random. We show that:(a) no
weakly 2-random real computes a perfect pathwise-random tree; it follows that the class of …

We study algorithmically random closed subsets of $2^\omega $, algorithmically random
continuous functions from $2^\omega $ to $2^\omega $, and algorithmically random Borel …

The study of Martin‐Löf randomness on a computable metric space with a computable
measure has seen much progress recently. In this paper we study Martin‐Löf randomness …

TOPICS IN ALGORITHMIC RANDOMNESS AND EFFECTIVE PROBABILITY A Dissertation
Submitted to the Graduate School of the University of Page 1 TOPICS IN ALGORITHMIC …

2.1. Computable analysis on R 2.2. Martin-Lof randomness and Schnorr randomness 2.3.
Other algorithmic randomness notions 3. Randomness and constructive mathematics 3.1 …

In this article, we study several aspects of the intersections of algorithmically random closed
sets. First, we answer a question of Cenzer and Weber, showing that the operation of …

Recall that B is PA relative to A if B computes a member of every nonempty $\Pi^ 0_1 (A) $
class. This two-place relation is invariant under Turing equivalence and so can be thought of …

For a class of objects C with some effective encoding F: k ω→ C (where k ω is the space of
infinite k-ary sequences), an object c∈ C may be called algorithmically random if c has …