 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.An alternative proof that the Gaussian cylinder set measure is not a measure uses the Cameron–Martin theorem and a result on the quasi-invariance of measures.If "γ""H" = "γ" really were a measure, then the identity function on "H" would radonify that measure, thus making id