Example for a Measure on a Ball in Hilbert Space

The example proposed by Vishik and Fursikov constructs an integral over a ball \(\mathcal {B}_\rho \) with radius \(\rho \) in a separable Hilbert vector space \(\mathcal {H}\) equipped with a Schauder basis \(\lbrace {\mathbf {e}}^n(\mathbf {x}),n=0,\cdots \rbrace \) .