Abstract: | Let P be a probability distribution on a separable metric space (S,d). We study the following problem of approximation of a distribution P by a set from a given class A2
S
: W(A,P)
S
(d(x,A))P(dx)min
AA
, where is a nondecreasing function. A special case where A is a parametric class A={A():T} is considered in detail. Our main interest is to obtain convergence results for sequences {A
*
n
}, where A
*
n
is an optimal set for a measure P
n
satisfying P
n
P, as n. |