 Continuity of lottery preferences

One standard mixture formulation says that if $A⪰B⪰C$, some $p\in [0,1]$ satisfies $B\sim pA+(1-p)C$. Under the other Von Neumann-Morgenstern utility theorem assumptions, this excludes lexicographic comparisons and permits numerical utility function scales. It concerns mixtures of lotteries, rather than continuity of a monetary utility function on a prespecified consumption domain.