• Regularities of Multifractal Measures

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/118/02/0273-0279

    • Keywords

       

      Multifractal measures; decomposition theorem; Hausdorff measure; packing measure; regularity.

    • Abstract

       

      First, we prove the decomposition theorem for the regularities of multifractal Hausdorff measure and packing measure in $\mathbb{R}^d$. This decomposition theorem enables us to split a set into regular and irregular parts, so that we can analyze each separately, and recombine them without affecting density properties. Next, we give some properties related to multifractal Hausdorff and packing densities. Finally, we extend the density theorem in [6] to any measurable set.

    • Author Affiliations

       

      Hun Ki Baek1

      1. Department of Mathematics, Kyungpook National University, 702-701, South Korea
    • Dates

       
  • Proceedings – Mathematical Sciences | News

© 2017-2019 Indian Academy of Sciences, Bengaluru.