Explicit approximation of the symmetric rearrangement by polarizations

We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial function.      

On Almost Sure Convergence of Series of Random Variables Irrespective of Their Joint Distributions

In this article, necessary and sufficient conditions are presented for a series of random variables to converge absolutely almost surely irrespective of their joint distributions. The summands are not assumed to be integrable. Illustrative examples and counterexamples are presented.     

A random approximation of set valued càdlàg functions

In this paper we study the problem of estimating a càdlàg function f whose values are compact convex sets. For this purpose a random selection of points in the interval [0,1] is considered and for each selected point x, a random sample in f(x). On the basis of this a sequence of approximants f_n,m is constructed (where n and m are the respective sample sizes). Under general conditions, rates of convergence are obtained for Skorokhod's J₁ topology, and in case of continuity of the estimated function also for the uniform one.     

Almost Sure Convergence of the General Jamison Weighted Sum of $$ {\user1{B}} $$-Valued Random Variables

In this paper．two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods．their properties and relationships are systematically discussed．We also analysed the implication of the conditions in previous papers．Then we apply these consequences to B-valued random variables．and greatly improve the original results of the strong convergence of the general Janfison weighted sum．Furthermore,our discussions are useful to the corresponding questions of real-valued random variables．