  We present a theory of backward stochastic differential equations in
continuous time with an arbitrary filtered probability space. No assumptions
are made regarding the left continuity of the filtration, of the predictable
quadratic variations of martingales or of the measure integrating the driver.
We present conditions for existence and uniqueness of square-integrable
solutions, using Lipschitz continuity of the driver. These conditions unite the
requirements for existence in continuous and discrete time and allow discrete
processes to be embedded with continuous ones. We also present conditions for a
comparison theorem and hence construct time consistent nonlinear expectations
in these general spaces.
