A finite-dimentional problem of embedding the largest by the inclusion of lower Lebesgue set of given convex function f(x) in a given convex body D ⊂ R p is considered. This problem is the generalization of the problem of inscribed ball (function f(x) is some norm, and the Lebesgue sets are the corresponding balls). The function f(x) must be differentiable on R p possibly expending the point 0 p and 0 p is the uniqueness point of minimum. Mathematical formalization of this problem is proposed in the form of finding maximin of a function of the difference of arguments.
