Affiliation:
1. Akaki Tsereteli State University , 59 Tamar Mepe Str. , Kutaisi 4600 , Georgia
Abstract
Abstract
It is known that a translation invariant density differentiation basis B formed of convex sets and its Busemann–Feller extension
B
BF
{B_{\operatorname{BF}}}
have similar properties, in particular, the Busemann–Feller extension differentiates the same class of non-negative functions as the basis B. We prove the optimality of the convexity condition in this result.