Some examples of cylindrical measure without measurable norms (Q797716)

In the preceding paper [J. Math. Anal. Appl. 98, 158-165 (1984; Zbl 0527.28016)], the author offered the following problem. ''For each cylindrical measure, does there exist a continuous norm which is measurable (in the sense of Gross or Dudly-Feldman-Le Cam) with respect to this cylindrical measure?'' Here this problem is solved negatively. The author shows the existence of a cylindrical measure on a Hilbert space for which no continuous norm is measurable in any sense.