科研之友
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摘要
It is proved in the paper that different natural Fourier transforms (FTs) of the measure mentioned in the title are not continuous with respect to such sufficient topologies as Sazonov and Gross-Sazonov (introduced by Smolyanov [Gross-Sazonov theorem for alternating cylindrical measures, Vestnik Moskov. Univ. (4) (1983) 4-12]) topologies. The motivation of the result is the fact that the FT of the standard Wiener measure is discontinuous in a known sufficient topologies as stated by Smolyanov and Fomin (see e. g., [Measures on Topological Linear Spaces, Uspekhi Mat. Nauk 31(4) (1976) 3-56]).
- 出版日期2013-3
