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all B^^8(R°°). Moreover if /j, is ^-quasi-invariant, then {/*}re/zi also can be chosen as ^-quasi-invariant measures. Starting from this fundamental fact, we proceeded to the following general problem. Let R^d0dR> and 0 be a complete separable metric linear topological space whose topology is stronger than the usual topology of R°°. If fj. is $ -quasi-invariant, then does the same hold for almost all ft ? In the case that 72" is not dense in 0, it was easily shown that this problem is negative in general. However in the case that R°S is dense in 0, it was left as an open problem. In this paper we shall show that it is also negative, even if 0=l, by constructing a suitable /*.

Remark to the previous paper: ``Ergodic decomposition of quasi-invariant measures''