Solving stochastic convex feasibility problems in Hilbert spaces

In a stochastic convex feasibility problem connected with a complete probability space (Omega, A, mu) and a family of closed convex sets {C-omega}(omega is an element of Omega) in a real Hilbert space H, one wants to find a point that belongs to C-omega for mu-almost all omega is an element of Omega. We present a projection-based method where the variable relaxation parameter is defined by a geometrical condition, leading to an iteration sequence that is always weakly convergent to a mu-almost common point. We then give a general condition assuring norm convergence of this sequence to that mu-almost common point.