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We study in this paper a control problem in a space of random variables. Weshow that its Hamilton Jacobi Bellman equation is related to the Masterequation in Mean field theory. P.L. Lions in [14,15] introduced the Hilbertspace of square integrable random variables as a natural space for writing theMaster equation which appears in the mean field theory. W. Gangbo and A.\'Swi\k{e}ch [10] considered this type of equation in the space of probabilitymeasures equipped with the Wasserstein metric and use the concept ofWasserstein gradient. We compare the two approaches and provide some extensionof the results of Gangbo and \'Swi\k{e}ch.

Control Problem on Space of Random Variables and Master Equation