Sounds like a special case of crisp infradistributions (ie, all partial probability distributions have a unique associated crisp infradistribution)

Given some Q, we can consider the (nonempty) set of probability distributions equal to Q where Q is defined. This set is convex (clearly, a mixture of two probability distributions which agree with Q about the probability of an event will also agree with Q about the probability of an event).

Convex (compact) sets of probability distributions = crisp infradistributions.

Sounds like a special case of crisp infradistributions (ie, all partial probability distributions have a unique associated crisp infradistribution)

Given some Q, we can consider the (nonempty) set of probability distributions equal to Q where Q is defined. This set is convex (clearly, a mixture of two probability distributions which agree with Q about the probability of an event will also agree with Q about the probability of an event).

Convex (compact) sets of probability distributions = crisp infradistributions.