%0 Journal Article
%T Brouwer Fixed Point Theorem in (L^0)^d
%A Samuel Drapeau
%A Martin Karliczek
%A Michael Kupper
%A Martin Streckfu£¿
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1305.2890v3