The fluctuation theorem (FT) describes how a system's thermodynamic irreversibility develops in time from a completely thermodynamically reversible system at short observation times, to a thermodynamically irreversible one at infinitely long times. In this paper, we present a general definition of the dissipation function Vt, the quantitative argument in the fluctuation theorem (FT), that is a measure of a system's irreversibility. Originally cast for deterministic systems, we demonstrate, through the example of two recent experiments, that the dissipation function can be defined for stochastic systems. While the ensemble average of Vt is positive definite irrespective of the system for which it is constructed, different expressions for Vt can arise in stochastic and deterministic systems. Moreover, within the stochastic framework, Vt is not unique. Nevertheless, each of these expressions for Vt satisfies the FT.