This paper provides results on the minimal robust positively invariant set and its robust positively invariant approximations of an asymptotically stable, continuous-time, linear time-invariant system. The minimal robust positively invariant set is characterized as an infinite time Aumann Integral. A novel family of robust positively invariant sets, defined as a simple scaling of a finite time Aumann Integral, is characterized. Adequate members of this family are robust positively invariant sets and are arbitrarily close outer approximations of the minimal robust positively invariant set. A practical result, based on the optimal control theory, for the construction of safe polytopic sets is also provided. Computational procedures are briefly discussed and some simple, illustrative, examples are provided.