Generalized rotationally quasi-invariant cylindrical measures (Q1076185)

There are two concepts of measurable norm. One was introduced by L. Gross, and the other by Dudley-Feldman-le Cam. In 1974, Badrikian-Chevet offered the following problem: Do these two measurabilities coincide with each other for every cylindrical measure? The author showed the existence of the counterexample to this question. However the problem of finding a largest class of cylindrical measures for which two measurabilities are equivalent is unsolved. The author introduces a new concept ''generalized rotationally quasi-invariant cylindrical measure'', and investigates the characterization of this cylindrical measure. And also, she shows that two measurabilities are equivalent for every generalized rotationally quasi-invariant cylindrical measure.