I have been reading the article "A peak set of Hausdorff dimension $2n-1$ for the algebra $A(\mathcal{D})$ in the boundary of a domain $\mathcal{D}$ with $C^\infty$-boundary in $\mathbb{C}^n$" by B. S. Henriksen. It is a short paper but quite dense in my opinion.
But I have a problem with some of the definitions. For example in the begining of page 275 there are three definitions that to me look circular. I have not seen anything similar before. Does anyone has a better understanding of this part ? 
