Iterative averaging of entropic projections for solving stochastic convex feasibility problems

The problem considered in this paper is that of finding a point which is common to almost all the members of a measurable family of closed convex subsets of Rⁿ++, provided that such a point exists. The main results show that this problem can be solved by an iterative method essentially based on averaging at each step the Bregman projections with respect f(x) = Σⁿi=l xi·lnxi of the current iterate onto the given sets.