  Martin-Lof's definition of random sequences of cbits as those not belonging
to any set of constructive zero Lebesgue measure is reformulated in the
language of Algebraic Probability Theory.
  The adoption of the Pour-El Richards theory of computability structures on
Banach spaces allows us to give a natural noncommutative extension of
Martin-Lof's definition, characterizing the random elements of a chain Von
Neumann algebra.
  In the particular case of the minimally informative noncommutative alphabet
our definition reduces to the definition of a random sequence of qubits.
