Asymptotic behavior of Laplace integrals and geometric characteristics of convex functions

The asymptotic behavior of Laplace integrals and geometric characteristics of convex functions are analyzed. The results show that the set of points on a convex space onto a convex space is defined by a convex function depending on the Laplace integral. It is also shown that the convex set contains the origin and the convex space is the supreme of the convex points in the convex domain. In the one-dimensional case, the volume distance is considered in more detail and give definitions that are in a sense equivalent.