4. (10 points) Let (, F, P; F) be a filtered space and M a process defined on the filtered space. Answer the following questions. a. There are three conditions for M to be a martingale with respect to F: (i) adapted to F, (ii) integrable, and (iii) this. State the third condition. b. Briefly explain why martingales are important in the study of stochastic pro- cesses. Hint: It suffices to state the name of the relevant mathematical result.