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The inverse isoperimetric problem of the entropy functional is considered in this Correspondence. This problem can be stated as follows: Given a known probability density function (pdf), what prior constraints are needed in order for this pdf to be the one that maximizes the entropy functional? The solution is given in terms of a Theorem, and it is compared to the Rozenberg-Rubichev solution. The Theorem is also used in simple applications, one of which illuminates the relationship of the maximum entropy principle (MEP) to the concept of "relative frequencies."