Probabilistic linear widths of Sobolev space with Jacobi weights on [-1,1]

Optimal asymptotic orders of the probabilistic linear (n, delta)-widths of lambda(n,delta)(W'(2,alpha,beta), nu, L-q,L-alpha,L-beta) of the weighted Sobolev space W'(2,alpha,beta) equipped with a Gaussian measure. are established, where L-q,L-alpha,L-beta, 1 <= q <= infinity, denotes the L-q space on [-1, 1] with respect to the measure (1-x)(alpha)(1 + x)(beta), alpha, beta > -1/2.