Recent characterizations of probability measures by use of conditional expectations have included many probability measures defined on subsets of the real line. This paper contains results which allow similar characterizations by use of conditional expectations but are valid for probability measures defined on subsets of an arbitrary space. In the special case of a measure defined on subsets of R' the result is not always as sharp as known results, but these theorems can be applied to measures defined on subsets of Rn with n ≧ 1.
