  Throughout the focus will be on a simple binary process, which has only two types of outcome \(O = \{0,1\}\). (The theory of randomness for the outcome sequences of such a simple process can be extended to more complicated sets of outcomes, but there is much of interest even in the question which binary sequences are product random?) A sequence of outcomes is an ordered collection of events, finite or infinite, such that each event is of a type in \(O\). So a sequence \(x = x_1 x_2 \ldots x_k\ldots\), where each \(x_i \in O\). The set of all infinite binary sequences of outcomes is known as the Cantor space. One familiar example of a process the outcomes of which form a Cantor space is an infinite sequence of independent flips of a fair coin, where 1 denotes heads and 0 tails. Notions from measure theory and computability theory are used in the discussion below; an elementary presentation of the mathematics needed can be found in supplement  B.2.