Continuous evolution families

Recently in relation to the theory of non-commutative probability, notion evolution family { ω s , t stretchy="false">} ≤ \{\omega _{s,t}\}_{s \le t} is generalized assuming only continuity parameters, namely alttext="left-parenthesis right-parenthesis right-arrow from bar stretchy="false">( stretchy="false">) stretchy="false">↦<!-- ↦ encoding="application/x-tex">(s,t) \mapsto \omega _{s,t} continuous with respect locally uniform convergence on a planar domain. In this article we present various equivalence conditions families concerned left and right parameters. We also provide an example discontinuous last section.