Title: Non-trivial lower bound for the depth of a centerline.

Abstract: By the centerpoint theorem the depth of a centerline in $R^d$ for
any
probability measure is at least $\frac{1}{d}$.
We improve slightly ($\frac{1}{d} + \frac{1}{3d^3}$)on this trivial lower
bound.
This is a joint work with Alexander Magazinov.