WALD’s famous sequential probability ratio test for comparing two simple hypotheses $P_1$ and $P_2$ is extended to the case when instead of successive observations of i.i.d. random variables general observations can be taken and final decisions are allowed at a discrete series of pre-assigned time points. It is shown that the following properties are equivalent:

(a) Each test of that type is closed.

(b) The errors of first and second kind of those tests can be made arbitrarily small.

(c) $P_1$ and $P_2$ are orthogonal probability measures.

This result is applied to the risk process in insurance mathematics and a uniqueness problem is discussed.