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 : "H" → "H" into an abstract Wiener space. By the Cameron–Martin theorem, "γ" would then be quasi-invariant under translation by any element of "H", which implies that either "H" is finite-dimensional or that "γ" is the zero measure. In either case, we have a contradiction.