In his paper 'On the Structure of Linear Models' Solow makes extensive use of some results about the characteristic roots of indecomposable nonnegative matrices which are due to Frobenius. A recent paper by Helmut Wielandt gives a drastically simplified proof of these results of Frobenius; moreover, in several places the results are sharpened. One of the purposes of writing this note is to bring this paper and its translation into English by Herstein to the attention of economists. Debreu and Herstein have succeeded in simplifying even further the proof of these results. It is pointed out here how these results are applicable in either simplifying, or obviating the need of, several of Solow's proofs.

Previous treatments of this approach brought topological considerations of the prospects space into the axioms. In this paper considerations of the topology of the prospect space itself are removed, the previous axioms are weakened an infinite number of sure prospects are allowed. On the basis of these axioms the existence of a measurable utility is established.