Carriers of continuous measures in a Hilbertian norm

Summary. From the standpoint of the theory of measures on the dual space of a nuclear space, we discuss the carrier of Wiener measure, regarding it as a measure on (3)') ( = Schwartz's space of distributions). This may be contrasted with the usual treatment which regards it as a measure on the space of paths. It is shown that for a>-=-9 integral operator Ia is nuclear on £ L2((0, 1)) ( = H0). Using this fact, we see that Wiener measure lies on the space IB(H0) (/3 0, and L be its subspace which is dense and nuclear in HQ. It means that there exists a complete orthonormal system {%k} in H0 and a sequence of positive numbers {ak} such that j[] a] < oo and the norm oo /£ £ \Z k=l