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ON (αn) -REGULAR SETS by tuomo.ojala is a document available to read on EtoBox.
This paper defines (αn)-regular sets in uniformly perfect metric spaces and establishes necessary and sufficient conditions for these sets to be classified as fat or thin. The main theorem states that an (αn)-regular set is fat if and only if (αn) belongs to ℓ0, and thin if (αn) does not belong to ℓ∞. Additionally, the paper discusses the implications of doubling measures on these sets and provides examples, including Sierpinski carpets and Cantor sets.
- Author
- tuomo.ojala
- Language
- EN