The Gross–Sazonov theorem for sign-variable cylindrical measures
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (1983), pp. 4-12
A topological condition is found whose fulfilment is sufficient for $\sigma$-additivity of bounded signed cylindrical measures. The topology $\tau_{\mathrm{C}\Gamma}$ used in this condition is in general strictly stronger than Sazonov's topology; however, $\tau_{\mathrm{C}\Gamma}$-continuity of the Fourier transformation of a cylindrical measure entails its $\tau_{\mathrm{C}}$-continujty.
@article{VMUMM_1983_4_a1,
author = {O. G. Smolyanov},
title = {The {Gross{\textendash}Sazonov} theorem for sign-variable cylindrical measures},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {4--12},
year = {1983},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_1983_4_a1/}
}
O. G. Smolyanov. The Gross–Sazonov theorem for sign-variable cylindrical measures. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (1983), pp. 4-12. http://geodesic.mathdoc.fr/item/VMUMM_1983_4_a1/