On an equivalence for differentiation bases of dyadic rectangles
Grigori Artashesovich Karagulyan, Davit Karagulyan, Mher Safaryan · Colloquium Mathematicum · 2016
The paper considers differentiation properties of rare bases of dyadic rectangles corresponding to increasing sequences $\{ u_k\}$ of integers. We prove that the condition \begin{equation*} \sup_k( u_{k+1}- u_k) \lt \infty \end{equation*} is necessary