Hilbert supports of Wiener measure (Q1316880)

Let \(w\) be the classical Wiener measure on \(X = C_ 0([0, \pi])\). It is well-known that if \(H\) is a Hilbert space and \(u:H \to X\) is a continuous linear operator, then \(w(u(H)) = 0\). The author shows that there is a Hilbert space \(H\) and a noncontinuous linear injection \(v:H \to X\) such that \(v(H)\) is \(w\)-measurable, \(v^{-1} : v(H) \to H\) is continuous and \(w(v(H)) = 1\).