Abstract
Some of the properties of extremum functions and their applications to Bayesian decision problems are discussed. Suppose that a conditional probability P (|y) over state space X, given some information y, is specified. Let f (x, u) be the performance index, where u is the decision variable. It turns out that the minimum of the conditional expectation Ex|y {f(x, u)} with respect to u is measurable so that the expectation Ey minu Ex|y {f(x, u)} can be taken. It is also shown that a measurable functionn u(y) can be chosen in such a way that u(y) minimizes Ex|y {f(x, u)} A class of min-max decision problems is also discussed.
