  We propose a two-point flux approximation finite-volume scheme for a
stochastic non-linear parabolic equation with a multiplicative noise. The time
discretization is implicit except for the stochastic noise term in order to be
compatible with stochastic integration in the sense of It\^{o}. We show
existence and uniqueness of solutions to the scheme and the appropriate
measurability for stochastic integration follows from the uniqueness of
approximate solutions.
