  Recently in relation to the theory of non-commutative probability, a notion
of evolution families $\{\omega_{s,t}\}_{s \le t}$ is generalized that are only
continuous in parameters, namely $(s,t) \mapsto \omega_{s,t}$ is continuous
with respect to locally uniform convergence on a planar domain. In this article
we present various equivalence conditions to the continuous evolution families
concerned with the left and right parameters. We also provide an example of a
discontinuous evolution family in the last section.
