Let

be the value function for the dynamic programming problem (example 2.32). Assume that
€¢ f is bounded on X × X
€¢ G(x) is nonempty for every x ˆŠ X
Show that v is a bounded functional on X (i.e., v ˆŠ B(X)) that satisfies the equation

for every x ˆŠ X.
The previous exercise showed that the value function satisfies Bellman's equation. The next exercise shows that every optimal plan must satisfy Bellman's equation at each stage.

Transcribed Image Text:

u(x)= sup U(x) yeG(x)