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.
D. H. Fremlin. M. Talagrand. "A Gaussian Measure on $l^\infty$." Ann. Probab. 8 (6) 1192 - 1193, December, 1980. https://doi.org/10.1214/aop/1176994583