  A probability space is a pair ($\mathcal{A},\phi $) where $\mathcal{A}$ is an
algebra and $\phi $ a state on the algebra. In classical probability
$\mathcal{A}$ is the algebra of linear combinations of indicator functions on
the sample space and in quantum probability $\mathcal{A}$ is the Heisenberg or
Clifford algebra. However, other algebras are of interest in non-commutative
probability. Here one discusses some other non-commutative probability spaces,
in particular those associated to non-commutative space-time.
