On the approximation of measurable linear functionals

Every Gaussian Radon measure (nonsymmetric) has the Riesz property. On R^∞, a shift μ₀ 1 σ_b of the law μ₀ of the Bernoulli sequence has the Riesz property iff $\text{b ? l}{}^2\text{or}\text{b ?}\text{R}{}_0{}^{\mathrm{\infty }}$.