Alternate dimensions aren’t outside our everyday experience. In fact, we can use exotic dimensions, like fractional dimensions, to measure things as common as coastlines. Find out about the Hausdorff ...

Geometric measure theory provides a framework for analysing the interplay between geometric structures and measure, and is particularly adept at characterising the complexity of fractal sets through ...

The work done in this paper is the result of an attempt to classify those functions $h$ for which the corresponding Hausdorff measure of $\mathscr{F} \lbrack 0,1 ...

We show that the σ-ideal of Borel subsets of ℝ³ of σ-finite 2-dimensional Hausdorff measure is not homogeneous. This partially answers a question of Zapletal. We prove that each of the statements ...

Multifractal analysis is a powerful mathematical framework that characterises the complex scaling properties inherent in many natural and engineered systems. By generalising the concept of fractal ...