On an equivalence for differentiation bases of dyadic rectangles
Volume 146 / 2017
Colloquium Mathematicum 146 (2017), 295-307
MSC: 42B08, 42B25.
DOI: 10.4064/cm6629-1-2016
Published online: 2 December 2016
Abstract
The paper considers differentiation properties of rare bases of dyadic rectangles corresponding to increasing sequences $\{\nu_k\}$ of integers. We prove that the condition \begin{equation*} \sup_k(\nu_{k+1}-\nu_k) \lt \infty \end{equation*} is necessary and sufficient for such a basis to be equivalent to the full basis of dyadic rectangles.
