Probabilistic Gel'fand Width

We defined the Gel'fand width under the probabilistic case setting, that is Let H be an Hilbert space,μis the Gaussian measure of H ,δ∈(0,1],we define the probabilistic Gel'fand ( n ,δ)-width (?). where Ln is the subspace of H with co dimension at most n ,μ(Gδ)≤δ.Afterwards we discussed the relationship between the linear width and the Gel'fand width,we obtain the asymptotic degree of Gel'fand width of R mand Sobolev space in Lq and S qspace under the probabilistic case setting.