The article on Arxiv makes no sense, it uses ill-defined notions, methods used there are contradictory, and most of the references it gives are from "Chaos, sol

The article on Arxiv makes no sense, it uses ill-defined notions, methods used there are contradictory, and most of the references it gives are from "Chaos, solitons and fractals" journal, which many professional mathematicians consider to be a joke. Mathematicians are great at handling infinities -- it just turns out that Lebesgue's measure is not usefyl when studying fractals. That's why other notions were introduced, like for instance Hausdorff dimension.