ON BANACH SUPPORT OF AN ERGODIC AND QUASI-INVARIANT MEASURE

Concerning the study of Banach support for the sample space of a random process, the idea can go back to the penetrating investigation of R. Dudley, V.N. Sudaso and X. Fernique, about Gaussian cylindrical measure. Gross, Ito, Sato and J. Kuelbs have investigated Banach support of a measure which, however, considers essentially Gaussian measure and proves that there exists Banach support for ordinary Gaussian measures. The abstract Wieber space introduced by Gross plays an important role in the study of Gaussian process. The ergodic and quasi-invariant measures investigated in this note are much wider than the abstract Wiener spaces, and the results obtained are stronger than the