  The classical Brouwer fixed point theorem states that in R^d every continuous
function from a convex, compact set on itself has a fixed point. For an
arbitrary probability space, let L^0 = L^0 (\Omega, A,P) be the set of random
variables. We consider (L^0)^d as an L^0-module and show that local,
sequentially continuous functions on closed and bounded subsets have a fixed
point which is measurable by construction.
