To study the representation of topological groups, it is natural to try to express a representation in terms of irreducible one. In general there exists representation that does not contain irreducible ones, however one can still try to express unitary representation as a "continuous sum" of irreducible representation in some sense. The SNAG theorem is such a result in the case the group is locally compact and abelian. It relies on the theory of projector-valued measure which we will explain in this talk before proving the SNAG theorem.