hypothesis tests

i wanted to know if hypothesis such as: H0: P(X belongs to V) = 0 and H1: P(X belongs to V) > 0,
can be used using typical hypothesis testing procedures. Here X is a random variable that
can take values from a given set, S, of integers and V is subset of values in S. The main question is: Given a sample from S, with known distribution, if some values, V, do not occur in the sample can i say with some given confidence that V does not occur in the population. In other words according to the sample distribution H1 should be true, but sample data shows otherwise. So, the missing data is really a property of the process generating this data.

P.S. sorry if i am breaking some principle assumptions of hypothesis testing...