Abstract: We deal with the so-called Ahlfors regular sets (also known as s-regular sets) in metric spaces. First we show that those sets correspond to a certain class of tree-like structures. Building on this observation we then study the following question: Under which conditions does the limit \lim_{\varepsilon\to 0+} \varepsilon^s N(\varepsilon,K) exist, where K is an s-regular set and N(\varepsilon,K) is for instance the \varepsilon-packing number of K?
Keywords: Ahlfors regular; s-regular; packing number; Minkowski measurability; renewal theory
DOI: DOI 10.14712/1213-7243.2022.011
AMS Subject Classification: 30L99 28A80