We give an example of a Gaussian measure on the $\sigma$-algebra of $l^\infty$ generated by all the continuous linear functionals on $l^\infty$, which is not a Radon measure.
@article{1176994583,
author = {Fremlin, D. H. and Talagrand, M.},
title = {A Gaussian Measure on $l^\infty$},
journal = {Ann. Probab.},
volume = {8},
number = {6},
year = {1980},
pages = { 1192-1193},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994583}
}
Fremlin, D. H.; Talagrand, M. A Gaussian Measure on $l^\infty$. Ann. Probab., Tome 8 (1980) no. 6, pp. 1192-1193. http://gdmltest.u-ga.fr/item/1176994583/