So the idea is take the general assumptions we have
for the infinite horizon problem,
and we're going to make the assumption that
the stage cost, g, is uniformly bounded
and left in below by some kind of constant, yeah, okay?
Moreover, we're going to assume that alpha
is strictly between zero and one,
so alpha represents a true discount cost.
We're going to see that under this assumption,
we can basically guarantee all three
of the criteria we have before that
the limit of convergence exists,
that we will have a necessary insufficient condition,
or sorry, we won't have a necessary condition
for the optimal value function,
to be the optimal value function.
It's actually a necessary insufficient.
And finally, we'll derive necessary insufficient conditions
for the optimal policy coming up.
All right, so let's look at this.