The canonical Gaussian cylinder set measure on an infinite-dimensional separable Hilbert space "H" does not correspond to a true measure on "H". The proof is quite simple: the ball of radius "r" (and center 0) has measure at most equal to that of the ball of radius "r" in an "n"-dimensional Hilbert space, and this tends to 0 as "n" tends to infinity. So the ball of radius "r" has measure 0; as the Hilbert space is a countable union of such balls it also has measure 0, which is a contradiction.