Geodesic
On an equivalence for differentiation bases of dyadic rectangles
G. A. Karagulyan1 ; D. A. Karagulyan1 ; M. H. Safaryan1
1 Institute of Mathematics Armenian National Academy of Sciences Baghramian ave. 24/5 0019, Yerevan, Armenia
Colloquium Mathematicum, Tome 146 (2017) no. 2, pp. 295-307.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm6629-1-2016
Keywords: paper considers differentiation properties rare bases dyadic rectangles corresponding increasing sequences integers prove condition begin equation* sup infty end equation* necessary sufficient basis equivalent full basis dyadic rectangles

G. A. Karagulyan 1 ; D. A. Karagulyan 1 ; M. H. Safaryan 1

1 Institute of Mathematics Armenian National Academy of Sciences Baghramian ave. 24/5 0019, Yerevan, Armenia 
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G. A. Karagulyan; D. A. Karagulyan; M. H. Safaryan. On an equivalence for differentiation bases of dyadic rectangles. Colloquium Mathematicum, Tome 146 (2017) no. 2, pp. 295-307. doi : 10.4064/cm6629-1-2016. http://geodesic.mathdoc.fr/articles/10.4064/cm6629-1-2016/

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