In this study, we will introduce an innovative and comprehensive multifractal framework,
substantiating counterparts to the classical findings in multifractal analysis and We embark …

By introducing a novel expression for the Hausdorff and packing measures with respect to
gauge functions, we establish a connection between different approaches to defining the …

Working with sets of infinite Ψ t-Hausdorff measures can be cumbersome, so simplifying
them to sets of positive finite general fractal measures proves to be highly beneficial. This …

The main aim of this paper is to present a comprehensive exploration of general multifractal
dimensions of Borel probability measures, with a specific emphasis on the diverse …

The main objective of this paper is to investigate the average general fractal dimensions of
typical compact metric spaces within the Gromov-Hausdorff space, using the Gromov …

This study takes a broad approach to the fractal geometry problem and proposes an intrinsic
definition of the general box dimensions and the general Hausdorff and packing dimensions …

In this research, we adopt a comprehensive approach to address the multifractal and fractal
analysis problem. We introduce a novel definition for the general Hausdorff and packing …

Let ν be a Borel probability measure on ℝ d and q, t∈ ℝ. This study takes a broad approach
to the multifractal and fractal analysis problem and proposes an intrinsic definition of the …

The objective of this research is to establish a representation of the general Hausdorff and
packing dimensions of compact sets in Euclidean space. This representation is formulated in …

Consider a separable metric space (X, d), and let (K (X), d˜) denote the space of non-empty
compact subsets of X equipped with the Hausdorff metric. This paper aims to introduce and …