Measures on infinite dimensional spaces? I am looking for a measures on an infinite dimensional space. In the process I came across the theorem structure theorem for Gaussian measure. The link for the theorem: https://en.wikipedia.org/wiki/Structure_theorem_for_Gaussian_measures
As I understand I have no other option but to stick to Gaussian measure. I want to have an intuitive idea why only Gaussian measure ( I did not quite the understand the proof, too mathematical) is possible. Any comments would be highly appreciated.

Depending on the space, measures may be fairly easy to come by. For example, if $B$ is any separable Banach space, let $\{a_n\}$ be a countable dense subset.  Then define, for any $E\subset B$,
$$\mu(E)=\sum_n 2^{-n}\,\delta_{a_n}(E),$$ where $\delta_{a_n}(E)=1$  if $a_n\in E$, and zero otherwise. Since weighted sums of measures are measures, $\mu$ is a probability measure on $B$.
Of course, any other set of weights may be used.
